diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index 898d18af56f0e..c33cd505d0948 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -590,6 +590,9 @@ Deprecations
 
 - :func:`pandas.api.types.is_categorical` is deprecated and will be removed in a future version; use `:func:pandas.api.types.is_categorical_dtype` instead (:issue:`33385`)
 - :meth:`Index.get_value` is deprecated and will be removed in a future version (:issue:`19728`)
+- :meth:`Series.dt.week` and `Series.dt.weekofyear` are deprecated and will be removed in a future version, use :meth:`Series.dt.isocalendar().week` instead (:issue:`33595`)
+- :meth:`DatetimeIndex.week` and `DatetimeIndex.weekofyear` are deprecated and will be removed in a future version, use :meth:`DatetimeIndex.isocalendar().week` instead (:issue:`33595`)
+- :meth:`DatetimeArray.week` and `DatetimeArray.weekofyear` are deprecated and will be removed in a future version, use :meth:`DatetimeArray.isocalendar().week` instead (:issue:`33595`)
 - :meth:`DateOffset.__call__` is deprecated and will be removed in a future version, use ``offset + other`` instead (:issue:`34171`)
 - Indexing an :class:`Index` object with a float key is deprecated, and will
   raise an ``IndexError`` in the future. You can manually convert to an integer key
diff --git a/pandas/core/arrays/datetimes.py b/pandas/core/arrays/datetimes.py
index 90088c370697e..50d792aeb12f4 100644
--- a/pandas/core/arrays/datetimes.py
+++ b/pandas/core/arrays/datetimes.py
@@ -1298,6 +1298,32 @@ def isocalendar(self):
             iso_calendar_df.iloc[self._isnan] = None
         return iso_calendar_df
 
+    @property
+    def weekofyear(self):
+        """
+        The week ordinal of the year.
+
+        .. deprecated:: 1.1.0
+
+        weekofyear and week have been deprecated.
+        Please use DatetimeIndex.isocalendar().week instead.
+        """
+        warnings.warn(
+            "weekofyear and week have been deprecated, please use "
+            "DatetimeIndex.isocalendar().week instead, which returns "
+            "a Series.  To exactly reproduce the behavior of week and "
+            "weekofyear and return an Index, you may call "
+            "pd.Int64Index(idx.isocalendar().week)",
+            FutureWarning,
+            stacklevel=3,
+        )
+        week_series = self.isocalendar().week
+        if week_series.hasnans:
+            return week_series.to_numpy(dtype="float64", na_value=np.nan)
+        return week_series.to_numpy(dtype="int64")
+
+    week = weekofyear
+
     year = _field_accessor(
         "year",
         "Y",
@@ -1482,14 +1508,6 @@ def isocalendar(self):
         dtype: int64
         """,
     )
-    weekofyear = _field_accessor(
-        "weekofyear",
-        "woy",
-        """
-        The week ordinal of the year.
-        """,
-    )
-    week = weekofyear
     _dayofweek_doc = """
     The day of the week with Monday=0, Sunday=6.
 
diff --git a/pandas/core/indexes/accessors.py b/pandas/core/indexes/accessors.py
index 598d228723ac8..881d5ce1fbaab 100644
--- a/pandas/core/indexes/accessors.py
+++ b/pandas/core/indexes/accessors.py
@@ -2,6 +2,7 @@
 datetimelike delegation
 """
 from typing import TYPE_CHECKING
+import warnings
 
 import numpy as np
 
@@ -250,6 +251,30 @@ def isocalendar(self):
         """
         return self._get_values().isocalendar().set_index(self._parent.index)
 
+    @property
+    def weekofyear(self):
+        """
+        The week ordinal of the year.
+
+        .. deprecated:: 1.1.0
+
+        Series.dt.weekofyear and Series.dt.week have been deprecated.
+        Please use Series.dt.isocalendar().week instead.
+        """
+        warnings.warn(
+            "Series.dt.weekofyear and Series.dt.week have been deprecated.  "
+            "Please use Series.dt.isocalendar().week instead.",
+            FutureWarning,
+            stacklevel=2,
+        )
+        week_series = self.isocalendar().week
+        week_series.name = self.name
+        if week_series.hasnans:
+            return week_series.astype("float64")
+        return week_series.astype("int64")
+
+    week = weekofyear
+
 
 @delegate_names(
     delegate=TimedeltaArray, accessors=TimedeltaArray._datetimelike_ops, typ="property"
diff --git a/pandas/tests/arrays/test_datetimelike.py b/pandas/tests/arrays/test_datetimelike.py
index d0bf5bb41bb2c..1a61b379de943 100644
--- a/pandas/tests/arrays/test_datetimelike.py
+++ b/pandas/tests/arrays/test_datetimelike.py
@@ -546,6 +546,9 @@ def test_bool_properties(self, datetime_index, propname):
 
     @pytest.mark.parametrize("propname", pd.DatetimeIndex._field_ops)
     def test_int_properties(self, datetime_index, propname):
+        if propname in ["week", "weekofyear"]:
+            # GH#33595 Deprecate week and weekofyear
+            return
         dti = datetime_index
         arr = DatetimeArray(dti)
 
diff --git a/pandas/tests/groupby/transform/test_transform.py b/pandas/tests/groupby/transform/test_transform.py
index e1042bf35acc4..7997247ca0307 100644
--- a/pandas/tests/groupby/transform/test_transform.py
+++ b/pandas/tests/groupby/transform/test_transform.py
@@ -1022,7 +1022,7 @@ def test_groupby_transform_with_datetimes(func, values):
     dates = pd.date_range("1/1/2011", periods=10, freq="D")
 
     stocks = pd.DataFrame({"price": np.arange(10.0)}, index=dates)
-    stocks["week_id"] = pd.to_datetime(stocks.index).week
+    stocks["week_id"] = dates.isocalendar().set_index(dates).week
 
     result = stocks.groupby(stocks["week_id"])["price"].transform(func)
 
diff --git a/pandas/tests/indexes/datetimes/test_misc.py b/pandas/tests/indexes/datetimes/test_misc.py
index 42a72125ba411..b9373328eb87f 100644
--- a/pandas/tests/indexes/datetimes/test_misc.py
+++ b/pandas/tests/indexes/datetimes/test_misc.py
@@ -156,8 +156,8 @@ def test_datetimeindex_accessors(self):
             assert dti.dayofyear[0] == 1
             assert dti.dayofyear[120] == 121
 
-            assert dti.weekofyear[0] == 1
-            assert dti.weekofyear[120] == 18
+            assert dti.isocalendar().week[0] == 1
+            assert dti.isocalendar().week[120] == 18
 
             assert dti.quarter[0] == 1
             assert dti.quarter[120] == 2
@@ -192,7 +192,7 @@ def test_datetimeindex_accessors(self):
             assert len(dti.microsecond) == 365
             assert len(dti.dayofweek) == 365
             assert len(dti.dayofyear) == 365
-            assert len(dti.weekofyear) == 365
+            assert len(dti.isocalendar()) == 365
             assert len(dti.quarter) == 365
             assert len(dti.is_month_start) == 365
             assert len(dti.is_month_end) == 365
@@ -205,6 +205,9 @@ def test_datetimeindex_accessors(self):
 
             # non boolean accessors -> return Index
             for accessor in DatetimeIndex._field_ops:
+                if accessor in ["week", "weekofyear"]:
+                    # GH#33595 Deprecate week and weekofyear
+                    continue
                 res = getattr(dti, accessor)
                 assert len(res) == 365
                 assert isinstance(res, Index)
@@ -285,7 +288,7 @@ def test_datetimeindex_accessors(self):
         dates = ["2013/12/29", "2013/12/30", "2013/12/31"]
         dates = DatetimeIndex(dates, tz="Europe/Brussels")
         expected = [52, 1, 1]
-        assert dates.weekofyear.tolist() == expected
+        assert dates.isocalendar().week.tolist() == expected
         assert [d.weekofyear for d in dates] == expected
 
     # GH 12806
@@ -383,6 +386,15 @@ def test_iter_readonly():
     list(dti)
 
 
+def test_week_and_weekofyear_are_deprecated():
+    # GH#33595 Deprecate week and weekofyear
+    idx = pd.date_range(start="2019-12-29", freq="D", periods=4)
+    with tm.assert_produces_warning(FutureWarning):
+        idx.week
+    with tm.assert_produces_warning(FutureWarning):
+        idx.weekofyear
+
+
 def test_isocalendar_returns_correct_values_close_to_new_year_with_tz():
     # GH 6538: Check that DatetimeIndex and its TimeStamp elements
     # return the same weekofyear accessor close to new year w/ tz
diff --git a/pandas/tests/indexes/datetimes/test_scalar_compat.py b/pandas/tests/indexes/datetimes/test_scalar_compat.py
index 21ee8649172da..e5d1277aed9cd 100644
--- a/pandas/tests/indexes/datetimes/test_scalar_compat.py
+++ b/pandas/tests/indexes/datetimes/test_scalar_compat.py
@@ -40,8 +40,6 @@ def test_dti_date_out_of_range(self, data):
         [
             "dayofweek",
             "dayofyear",
-            "week",
-            "weekofyear",
             "quarter",
             "days_in_month",
             "is_month_start",
@@ -59,6 +57,12 @@ def test_dti_timestamp_fields(self, field):
         result = getattr(Timestamp(idx[-1]), field)
         assert result == expected
 
+    def test_dti_timestamp_isocalendar_fields(self):
+        idx = tm.makeDateIndex(100)
+        expected = tuple(idx.isocalendar().iloc[-1].to_list())
+        result = idx[-1].isocalendar()
+        assert result == expected
+
     def test_dti_timestamp_freq_fields(self):
         # extra fields from DatetimeIndex like quarter and week
         idx = tm.makeDateIndex(100)
diff --git a/pandas/tests/scalar/test_nat.py b/pandas/tests/scalar/test_nat.py
index 5a92ee37342d5..e1e2ea1a5cec8 100644
--- a/pandas/tests/scalar/test_nat.py
+++ b/pandas/tests/scalar/test_nat.py
@@ -66,6 +66,9 @@ def test_nat_vector_field_access():
         # on NaT/Timestamp for compat with datetime
         if field == "weekday":
             continue
+        if field in ["week", "weekofyear"]:
+            # GH#33595 Deprecate week and weekofyear
+            continue
 
         result = getattr(idx, field)
         expected = Index([getattr(x, field) for x in idx])
@@ -78,6 +81,9 @@ def test_nat_vector_field_access():
         # on NaT/Timestamp for compat with datetime
         if field == "weekday":
             continue
+        if field in ["week", "weekofyear"]:
+            # GH#33595 Deprecate week and weekofyear
+            continue
 
         result = getattr(ser.dt, field)
         expected = [getattr(x, field) for x in idx]
diff --git a/pandas/tests/series/test_api.py b/pandas/tests/series/test_api.py
index a6430b4525d4a..042841bb4e019 100644
--- a/pandas/tests/series/test_api.py
+++ b/pandas/tests/series/test_api.py
@@ -719,6 +719,9 @@ def test_dt_accessor_api_for_categorical(self):
                 tm.assert_equal(res, exp)
 
             for attr in attr_names:
+                if attr in ["week", "weekofyear"]:
+                    # GH#33595 Deprecate week and weekofyear
+                    continue
                 res = getattr(c.dt, attr)
                 exp = getattr(s.dt, attr)
 
diff --git a/pandas/tests/series/test_datetime_values.py b/pandas/tests/series/test_datetime_values.py
index 8b1f58414e175..0fd51b8828bc5 100644
--- a/pandas/tests/series/test_datetime_values.py
+++ b/pandas/tests/series/test_datetime_values.py
@@ -89,7 +89,8 @@ def compare(s, name):
         for s in cases:
             for prop in ok_for_dt:
                 # we test freq below
-                if prop != "freq":
+                # we ignore week and weekofyear because they are deprecated
+                if prop not in ["freq", "week", "weekofyear"]:
                     compare(s, prop)
 
             for prop in ok_for_dt_methods:
@@ -122,7 +123,8 @@ def compare(s, name):
         for prop in ok_for_dt:
 
             # we test freq below
-            if prop != "freq":
+            # we ignore week and weekofyear because they are deprecated
+            if prop not in ["freq", "week", "weekofyear"]:
                 compare(s, prop)
 
         for prop in ok_for_dt_methods:
@@ -687,3 +689,12 @@ def test_isocalendar(self, input_series, expected_output):
             expected_output, columns=["year", "week", "day"], dtype="UInt32"
         )
         tm.assert_frame_equal(result, expected_frame)
+
+
+def test_week_and_weekofyear_are_deprecated():
+    # GH#33595 Deprecate week and weekofyear
+    series = pd.to_datetime(pd.Series(["2020-01-01"]))
+    with tm.assert_produces_warning(FutureWarning):
+        series.dt.week
+    with tm.assert_produces_warning(FutureWarning):
+        series.dt.weekofyear