diff --git a/pandas/_libs/lib.pyx b/pandas/_libs/lib.pyx
index 37e83ddb0ffed..51a947f79ede2 100644
--- a/pandas/_libs/lib.pyx
+++ b/pandas/_libs/lib.pyx
@@ -716,6 +716,14 @@ cpdef ndarray[object] ensure_string_array(
         Py_ssize_t i = 0, n = len(arr)
 
     if hasattr(arr, "to_numpy"):
+
+        if hasattr(arr, "dtype") and arr.dtype.kind in ["m", "M"]:
+            # dtype check to exclude DataFrame
+            # GH#41409 TODO: not a great place for this
+            out = arr.astype(str).astype(object)
+            out[arr.isna()] = na_value
+            return out
+
         arr = arr.to_numpy()
     elif not isinstance(arr, np.ndarray):
         arr = np.array(arr, dtype="object")
diff --git a/pandas/tests/frame/methods/test_astype.py b/pandas/tests/frame/methods/test_astype.py
index 881f8db305240..bd71f0a0716b4 100644
--- a/pandas/tests/frame/methods/test_astype.py
+++ b/pandas/tests/frame/methods/test_astype.py
@@ -632,13 +632,9 @@ def test_astype_tz_object_conversion(self, tz):
         result = result.astype({"tz": "datetime64[ns, Europe/London]"})
         tm.assert_frame_equal(result, expected)
 
-    def test_astype_dt64_to_string(self, frame_or_series, tz_naive_fixture, request):
+    def test_astype_dt64_to_string(self, frame_or_series, tz_naive_fixture):
+        # GH#41409
         tz = tz_naive_fixture
-        if tz is None:
-            mark = pytest.mark.xfail(
-                reason="GH#36153 uses ndarray formatting instead of DTA formatting"
-            )
-            request.node.add_marker(mark)
 
         dti = date_range("2016-01-01", periods=3, tz=tz)
         dta = dti._data
@@ -660,6 +656,15 @@ def test_astype_dt64_to_string(self, frame_or_series, tz_naive_fixture, request)
         alt = obj.astype(str)
         assert np.all(alt.iloc[1:] == result.iloc[1:])
 
+    def test_astype_td64_to_string(self, frame_or_series):
+        # GH#41409
+        tdi = pd.timedelta_range("1 Day", periods=3)
+        obj = frame_or_series(tdi)
+
+        expected = frame_or_series(["1 days", "2 days", "3 days"], dtype="string")
+        result = obj.astype("string")
+        tm.assert_equal(result, expected)
+
     def test_astype_bytes(self):
         # GH#39474
         result = DataFrame(["foo", "bar", "baz"]).astype(bytes)