diff --git a/doc/source/whatsnew/v2.0.0.rst b/doc/source/whatsnew/v2.0.0.rst
index 0004bc92b349e..51ca5e32d3467 100644
--- a/doc/source/whatsnew/v2.0.0.rst
+++ b/doc/source/whatsnew/v2.0.0.rst
@@ -271,7 +271,7 @@ Removal of prior version deprecations/changes
 - Changed the behavior of :class:`Series` constructor, it will no longer infer a datetime64 or timedelta64 dtype from string entries (:issue:`41731`)
 - Changed behavior of :class:`Index` constructor when passed a ``SparseArray`` or ``SparseDtype`` to retain that dtype instead of casting to ``numpy.ndarray`` (:issue:`43930`)
 - Changed behavior of :meth:`DataFrame.any` and :meth:`DataFrame.all` with ``bool_only=True``; object-dtype columns with all-bool values will no longer be included, manually cast to ``bool`` dtype first (:issue:`46188`)
--
+- Enforced deprecation in :method:`DataFrame.mean` and :method:`DataFrame.median` dropping datetime64 and datetime64tz when ``numeric_only=None`` (:issue:`29941`)
 
 .. ---------------------------------------------------------------------------
 .. _whatsnew_200.performance:
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index fe6fda34a89ef..db436a4415842 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -124,7 +124,6 @@
     is_1d_only_ea_dtype,
     is_bool_dtype,
     is_dataclass,
-    is_datetime64_any_dtype,
     is_dict_like,
     is_dtype_equal,
     is_extension_array_dtype,
@@ -10739,29 +10738,6 @@ def _reduce(
         assert filter_type is None or filter_type == "bool", filter_type
         out_dtype = "bool" if filter_type == "bool" else None
 
-        if numeric_only is None and name in ["mean", "median"]:
-            own_dtypes = [arr.dtype for arr in self._mgr.arrays]
-
-            dtype_is_dt = np.array(
-                [is_datetime64_any_dtype(dtype) for dtype in own_dtypes],
-                dtype=bool,
-            )
-            if dtype_is_dt.any():
-                warnings.warn(
-                    "DataFrame.mean and DataFrame.median with numeric_only=None "
-                    "will include datetime64 and datetime64tz columns in a "
-                    "future version.",
-                    FutureWarning,
-                    stacklevel=find_stack_level(),
-                )
-                # Non-copy equivalent to
-                #  dt64_cols = self.dtypes.apply(is_datetime64_any_dtype)
-                #  cols = self.columns[~dt64_cols]
-                #  self = self[cols]
-                predicate = lambda x: not is_datetime64_any_dtype(x.dtype)
-                mgr = self._mgr._get_data_subset(predicate)
-                self = type(self)(mgr)
-
         # TODO: Make other agg func handle axis=None properly GH#21597
         axis = self._get_axis_number(axis)
         labels = self._get_agg_axis(axis)
diff --git a/pandas/tests/frame/test_reductions.py b/pandas/tests/frame/test_reductions.py
index 6a4af7a8cd32e..a7e0a0df021a8 100644
--- a/pandas/tests/frame/test_reductions.py
+++ b/pandas/tests/frame/test_reductions.py
@@ -74,15 +74,12 @@ def assert_stat_op_calc(
     f = getattr(frame, opname)
 
     if check_dates:
-        expected_warning = FutureWarning if opname in ["mean", "median"] else None
         df = DataFrame({"b": date_range("1/1/2001", periods=2)})
-        with tm.assert_produces_warning(expected_warning):
-            result = getattr(df, opname)()
+        result = getattr(df, opname)()
         assert isinstance(result, Series)
 
         df["a"] = range(len(df))
-        with tm.assert_produces_warning(expected_warning):
-            result = getattr(df, opname)()
+        result = getattr(df, opname)()
         assert isinstance(result, Series)
         assert len(result)
 
@@ -384,21 +381,16 @@ def test_nunique(self):
     def test_mean_mixed_datetime_numeric(self, tz):
         # https://github.com/pandas-dev/pandas/issues/24752
         df = DataFrame({"A": [1, 1], "B": [Timestamp("2000", tz=tz)] * 2})
-        with tm.assert_produces_warning(FutureWarning):
-            result = df.mean()
-        expected = Series([1.0], index=["A"])
+        result = df.mean()
+        expected = Series([1.0, Timestamp("2000", tz=tz)], index=["A", "B"])
         tm.assert_series_equal(result, expected)
 
     @pytest.mark.parametrize("tz", [None, "UTC"])
-    def test_mean_excludes_datetimes(self, tz):
+    def test_mean_only_datetimes(self, tz):
         # https://github.com/pandas-dev/pandas/issues/24752
-        # Our long-term desired behavior is unclear, but the behavior in
-        # 0.24.0rc1 was buggy.
         df = DataFrame({"A": [Timestamp("2000", tz=tz)] * 2})
-        with tm.assert_produces_warning(FutureWarning):
-            result = df.mean()
-
-        expected = Series(dtype=np.float64)
+        result = df.mean()
+        expected = Series([Timestamp("2000", tz=tz)], index=["A"])
         tm.assert_series_equal(result, expected)
 
     def test_mean_mixed_string_decimal(self):
@@ -864,10 +856,8 @@ def test_mean_datetimelike(self):
         expected = Series({"A": 1.0})
         tm.assert_series_equal(result, expected)
 
-        with tm.assert_produces_warning(FutureWarning):
-            # in the future datetime columns will be included
-            result = df.mean()
-        expected = Series({"A": 1.0, "C": df.loc[1, "C"]})
+        result = df.mean()
+        expected = Series({"A": 1.0, "B": Timestamp("2016-01-02"), "C": df.loc[1, "C"]})
         tm.assert_series_equal(result, expected)
 
     def test_mean_datetimelike_numeric_only_false(self):