diff --git a/pandas/core/arrays/datetimelike.py b/pandas/core/arrays/datetimelike.py
index 83a9c0ba61c2d..1f11ca6d4cc8b 100644
--- a/pandas/core/arrays/datetimelike.py
+++ b/pandas/core/arrays/datetimelike.py
@@ -1556,6 +1556,28 @@ def mean(self, skipna=True):
         # Don't have to worry about NA `result`, since no NA went in.
         return self._box_func(result)
 
+    def median(self, axis: Optional[int] = None, skipna: bool = True, *args, **kwargs):
+        nv.validate_median(args, kwargs)
+
+        if axis is not None and abs(axis) >= self.ndim:
+            raise ValueError("abs(axis) must be less than ndim")
+
+        if self.size == 0:
+            if self.ndim == 1 or axis is None:
+                return NaT
+            shape = list(self.shape)
+            del shape[axis]
+            shape = [1 if x == 0 else x for x in shape]
+            result = np.empty(shape, dtype="i8")
+            result.fill(iNaT)
+            return self._from_backing_data(result)
+
+        mask = self.isna()
+        result = nanops.nanmedian(self.asi8, axis=axis, skipna=skipna, mask=mask)
+        if axis is None or self.ndim == 1:
+            return self._box_func(result)
+        return self._from_backing_data(result.astype("i8"))
+
 
 DatetimeLikeArrayMixin._add_comparison_ops()
 
diff --git a/pandas/core/arrays/timedeltas.py b/pandas/core/arrays/timedeltas.py
index c97c7da375fd4..f85e3e716bbf9 100644
--- a/pandas/core/arrays/timedeltas.py
+++ b/pandas/core/arrays/timedeltas.py
@@ -393,19 +393,6 @@ def std(
         result = nanops.nanstd(self._data, axis=axis, skipna=skipna, ddof=ddof)
         return Timedelta(result)
 
-    def median(
-        self,
-        axis=None,
-        out=None,
-        overwrite_input: bool = False,
-        keepdims: bool = False,
-        skipna: bool = True,
-    ):
-        nv.validate_median(
-            (), dict(out=out, overwrite_input=overwrite_input, keepdims=keepdims)
-        )
-        return nanops.nanmedian(self._data, axis=axis, skipna=skipna)
-
     # ----------------------------------------------------------------
     # Rendering Methods
 
diff --git a/pandas/tests/arrays/test_datetimes.py b/pandas/tests/arrays/test_datetimes.py
index e7605125e7420..9f136b4979bb7 100644
--- a/pandas/tests/arrays/test_datetimes.py
+++ b/pandas/tests/arrays/test_datetimes.py
@@ -454,8 +454,9 @@ def test_tz_dtype_matches(self):
 
 
 class TestReductions:
-    @pytest.mark.parametrize("tz", [None, "US/Central"])
-    def test_min_max(self, tz):
+    @pytest.fixture
+    def arr1d(self, tz_naive_fixture):
+        tz = tz_naive_fixture
         dtype = DatetimeTZDtype(tz=tz) if tz is not None else np.dtype("M8[ns]")
         arr = DatetimeArray._from_sequence(
             [
@@ -468,6 +469,11 @@ def test_min_max(self, tz):
             ],
             dtype=dtype,
         )
+        return arr
+
+    def test_min_max(self, arr1d):
+        arr = arr1d
+        tz = arr.tz
 
         result = arr.min()
         expected = pd.Timestamp("2000-01-02", tz=tz)
@@ -493,3 +499,70 @@ def test_min_max_empty(self, skipna, tz):
 
         result = arr.max(skipna=skipna)
         assert result is pd.NaT
+
+    @pytest.mark.parametrize("tz", [None, "US/Central"])
+    @pytest.mark.parametrize("skipna", [True, False])
+    def test_median_empty(self, skipna, tz):
+        dtype = DatetimeTZDtype(tz=tz) if tz is not None else np.dtype("M8[ns]")
+        arr = DatetimeArray._from_sequence([], dtype=dtype)
+        result = arr.median(skipna=skipna)
+        assert result is pd.NaT
+
+        arr = arr.reshape(0, 3)
+        result = arr.median(axis=0, skipna=skipna)
+        expected = type(arr)._from_sequence([pd.NaT, pd.NaT, pd.NaT], dtype=arr.dtype)
+        tm.assert_equal(result, expected)
+
+        result = arr.median(axis=1, skipna=skipna)
+        expected = type(arr)._from_sequence([pd.NaT], dtype=arr.dtype)
+        tm.assert_equal(result, expected)
+
+    def test_median(self, arr1d):
+        arr = arr1d
+
+        result = arr.median()
+        assert result == arr[0]
+        result = arr.median(skipna=False)
+        assert result is pd.NaT
+
+        result = arr.dropna().median(skipna=False)
+        assert result == arr[0]
+
+        result = arr.median(axis=0)
+        assert result == arr[0]
+
+    def test_median_axis(self, arr1d):
+        arr = arr1d
+        assert arr.median(axis=0) == arr.median()
+        assert arr.median(axis=0, skipna=False) is pd.NaT
+
+        msg = r"abs\(axis\) must be less than ndim"
+        with pytest.raises(ValueError, match=msg):
+            arr.median(axis=1)
+
+    @pytest.mark.filterwarnings("ignore:All-NaN slice encountered:RuntimeWarning")
+    def test_median_2d(self, arr1d):
+        arr = arr1d.reshape(1, -1)
+
+        # axis = None
+        assert arr.median() == arr1d.median()
+        assert arr.median(skipna=False) is pd.NaT
+
+        # axis = 0
+        result = arr.median(axis=0)
+        expected = arr1d
+        tm.assert_equal(result, expected)
+
+        # Since column 3 is all-NaT, we get NaT there with or without skipna
+        result = arr.median(axis=0, skipna=False)
+        expected = arr1d
+        tm.assert_equal(result, expected)
+
+        # axis = 1
+        result = arr.median(axis=1)
+        expected = type(arr)._from_sequence([arr1d.median()])
+        tm.assert_equal(result, expected)
+
+        result = arr.median(axis=1, skipna=False)
+        expected = type(arr)._from_sequence([pd.NaT], dtype=arr.dtype)
+        tm.assert_equal(result, expected)
diff --git a/pandas/tests/reductions/test_stat_reductions.py b/pandas/tests/reductions/test_stat_reductions.py
index 59dbcb9ab9fa0..fd2746672a0eb 100644
--- a/pandas/tests/reductions/test_stat_reductions.py
+++ b/pandas/tests/reductions/test_stat_reductions.py
@@ -96,7 +96,7 @@ def _check_stat_op(
             string_series_[5:15] = np.NaN
 
             # mean, idxmax, idxmin, min, and max are valid for dates
-            if name not in ["max", "min", "mean"]:
+            if name not in ["max", "min", "mean", "median"]:
                 ds = Series(pd.date_range("1/1/2001", periods=10))
                 with pytest.raises(TypeError):
                     f(ds)