diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index 10522ff797c59..2c792d5f10b00 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -776,6 +776,7 @@ Deprecations
   instead (:issue:`34191`).
 - The ``squeeze`` keyword in the ``groupby`` function is deprecated and will be removed in a future version (:issue:`32380`)
 - The ``tz`` keyword in :meth:`Period.to_timestamp` is deprecated and will be removed in a future version; use `per.to_timestamp(...).tz_localize(tz)`` instead (:issue:`34522`)
+- :meth:`DatetimeIndex.to_perioddelta` is deprecated and will be removed in a future version.  Use ``index - index.to_period(freq).to_timestamp()`` instead (:issue:`34853`)
 
 .. ---------------------------------------------------------------------------
 
diff --git a/pandas/core/arrays/datetimes.py b/pandas/core/arrays/datetimes.py
index b6c27abc321e1..461f71ff821fa 100644
--- a/pandas/core/arrays/datetimes.py
+++ b/pandas/core/arrays/datetimes.py
@@ -1125,7 +1125,14 @@ def to_perioddelta(self, freq):
         -------
         TimedeltaArray/Index
         """
-        # TODO: consider privatizing (discussion in GH#23113)
+        # Deprecaation GH#34853
+        warnings.warn(
+            "to_perioddelta is deprecated and will be removed in a "
+            "future version.  "
+            "Use `dtindex - dtindex.to_period(freq).to_timestamp()` instead",
+            FutureWarning,
+            stacklevel=3,
+        )
         from pandas.core.arrays.timedeltas import TimedeltaArray
 
         i8delta = self.asi8 - self.to_period(freq).to_timestamp().asi8
diff --git a/pandas/tests/arrays/test_datetimelike.py b/pandas/tests/arrays/test_datetimelike.py
index 1a61b379de943..b1ab700427c28 100644
--- a/pandas/tests/arrays/test_datetimelike.py
+++ b/pandas/tests/arrays/test_datetimelike.py
@@ -511,8 +511,13 @@ def test_to_perioddelta(self, datetime_index, freqstr):
         dti = datetime_index
         arr = DatetimeArray(dti)
 
-        expected = dti.to_perioddelta(freq=freqstr)
-        result = arr.to_perioddelta(freq=freqstr)
+        with tm.assert_produces_warning(FutureWarning):
+            # Deprecation GH#34853
+            expected = dti.to_perioddelta(freq=freqstr)
+        with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
+            # stacklevel is chosen to be "correct" for DatetimeIndex, not
+            #  DatetimeArray
+            result = arr.to_perioddelta(freq=freqstr)
         assert isinstance(result, TimedeltaArray)
 
         # placeholder until these become actual EA subclasses and we can use