diff --git a/doc/source/whatsnew/v1.0.2.rst b/doc/source/whatsnew/v1.0.2.rst
index f491774991090..e91bab0925bf7 100644
--- a/doc/source/whatsnew/v1.0.2.rst
+++ b/doc/source/whatsnew/v1.0.2.rst
@@ -23,6 +23,7 @@ Fixed regressions
 - Fixed regression where :func:`read_pickle` raised a ``UnicodeDecodeError`` when reading a py27 pickle with :class:`MultiIndex` column (:issue:`31988`).
 - Fixed regression in :class:`DataFrame` arithmetic operations with mis-matched columns (:issue:`31623`)
 - Fixed regression in :meth:`GroupBy.agg` calling a user-provided function an extra time on an empty input (:issue:`31760`)
+- Joining on :class:`DatetimeIndex` or :class:`TimedeltaIndex` will preserve ``freq`` in simple cases (:issue:`32166`)
 -
 
 .. ---------------------------------------------------------------------------
diff --git a/pandas/core/indexes/datetimelike.py b/pandas/core/indexes/datetimelike.py
index 349b582de4358..72a2aba2d8a88 100644
--- a/pandas/core/indexes/datetimelike.py
+++ b/pandas/core/indexes/datetimelike.py
@@ -910,17 +910,14 @@ def _is_convertible_to_index_for_join(cls, other: Index) -> bool:
             return True
         return False
 
-    def _wrap_joined_index(self, joined, other):
+    def _wrap_joined_index(self, joined: np.ndarray, other):
+        assert other.dtype == self.dtype, (other.dtype, self.dtype)
         name = get_op_result_name(self, other)
-        if self._can_fast_union(other):
-            joined = self._shallow_copy(joined)
-            joined.name = name
-            return joined
-        else:
-            kwargs = {}
-            if hasattr(self, "tz"):
-                kwargs["tz"] = getattr(other, "tz", None)
-            return type(self)._simple_new(joined, name, **kwargs)
+
+        freq = self.freq if self._can_fast_union(other) else None
+        new_data = type(self._data)._simple_new(joined, dtype=self.dtype, freq=freq)
+
+        return type(self)._simple_new(new_data, name=name)
 
     # --------------------------------------------------------------------
     # List-Like Methods
diff --git a/pandas/tests/indexes/datetimes/test_join.py b/pandas/tests/indexes/datetimes/test_join.py
index e4d6958dbd3d8..f2f88fd7dc90c 100644
--- a/pandas/tests/indexes/datetimes/test_join.py
+++ b/pandas/tests/indexes/datetimes/test_join.py
@@ -129,3 +129,16 @@ def test_naive_aware_conflicts(self):
 
         with pytest.raises(TypeError, match=msg):
             aware.join(naive)
+
+    @pytest.mark.parametrize("tz", [None, "US/Pacific"])
+    def test_join_preserves_freq(self, tz):
+        # GH#32157
+        dti = date_range("2016-01-01", periods=10, tz=tz)
+        result = dti[:5].join(dti[5:], how="outer")
+        assert result.freq == dti.freq
+        tm.assert_index_equal(result, dti)
+
+        result = dti[:5].join(dti[6:], how="outer")
+        assert result.freq is None
+        expected = dti.delete(5)
+        tm.assert_index_equal(result, expected)
diff --git a/pandas/tests/indexes/timedeltas/test_join.py b/pandas/tests/indexes/timedeltas/test_join.py
index 3e73ed35dae96..aaf4ef29e162b 100644
--- a/pandas/tests/indexes/timedeltas/test_join.py
+++ b/pandas/tests/indexes/timedeltas/test_join.py
@@ -35,3 +35,15 @@ def test_does_not_convert_mixed_integer(self):
         assert cols.dtype == np.dtype("O")
         assert cols.dtype == joined.dtype
         tm.assert_index_equal(cols, joined)
+
+    def test_join_preserves_freq(self):
+        # GH#32157
+        tdi = timedelta_range("1 day", periods=10)
+        result = tdi[:5].join(tdi[5:], how="outer")
+        assert result.freq == tdi.freq
+        tm.assert_index_equal(result, tdi)
+
+        result = tdi[:5].join(tdi[6:], how="outer")
+        assert result.freq is None
+        expected = tdi.delete(5)
+        tm.assert_index_equal(result, expected)