diff --git a/pandas/core/arrays/datetimes.py b/pandas/core/arrays/datetimes.py
index d3c0bbdf53310..fc894e1de0e37 100644
--- a/pandas/core/arrays/datetimes.py
+++ b/pandas/core/arrays/datetimes.py
@@ -226,13 +226,16 @@ class DatetimeArray(dtl.TimelikeOps, dtl.DatelikeOps):
     """
 
     _typ = "datetimearray"
-    _internal_fill_value = np.datetime64("NaT", "ns")
     _recognized_scalars = (datetime, np.datetime64)
     _is_recognized_dtype: Callable[[DtypeObj], bool] = lambda x: lib.is_np_dtype(
         x, "M"
     ) or isinstance(x, DatetimeTZDtype)
     _infer_matches = ("datetime", "datetime64", "date")
 
+    @property
+    def _internal_fill_value(self) -> np.datetime64:
+        return np.datetime64("NaT", self.unit)
+
     @property
     def _scalar_type(self) -> type[Timestamp]:
         return Timestamp
diff --git a/pandas/core/arrays/timedeltas.py b/pandas/core/arrays/timedeltas.py
index 514ad28f698d6..ff2e2e6429936 100644
--- a/pandas/core/arrays/timedeltas.py
+++ b/pandas/core/arrays/timedeltas.py
@@ -154,11 +154,14 @@ class TimedeltaArray(dtl.TimelikeOps):
     """
 
     _typ = "timedeltaarray"
-    _internal_fill_value = np.timedelta64("NaT", "ns")
     _recognized_scalars = (timedelta, np.timedelta64, Tick)
     _is_recognized_dtype: Callable[[DtypeObj], bool] = lambda x: lib.is_np_dtype(x, "m")
     _infer_matches = ("timedelta", "timedelta64")
 
+    @property
+    def _internal_fill_value(self) -> np.timedelta64:
+        return np.timedelta64("NaT", self.unit)
+
     @property
     def _scalar_type(self) -> type[Timedelta]:
         return Timedelta
diff --git a/pandas/tests/frame/methods/test_quantile.py b/pandas/tests/frame/methods/test_quantile.py
index eded9d9473385..df1f2a80e76e7 100644
--- a/pandas/tests/frame/methods/test_quantile.py
+++ b/pandas/tests/frame/methods/test_quantile.py
@@ -928,3 +928,12 @@ def test_multi_quantile_numeric_only_retains_columns():
     tm.assert_frame_equal(
         result, expected, check_index_type=True, check_column_type=True
     )
+
+
+@pytest.mark.parametrize("typ", ["datetime64", "timedelta64"])
+def test_quantile_empty_datetimelike(typ, unit):
+    dtype = f"{typ}[{unit}]"
+    df = DataFrame(np.array([], dtype=dtype))
+    result = df.quantile()
+    expected = Series([pd.NaT], name=0.5, dtype=dtype)
+    tm.assert_series_equal(result, expected)
diff --git a/pandas/tests/series/methods/test_quantile.py b/pandas/tests/series/methods/test_quantile.py
index fa0563271d7df..294437e557fdc 100644
--- a/pandas/tests/series/methods/test_quantile.py
+++ b/pandas/tests/series/methods/test_quantile.py
@@ -245,3 +245,10 @@ def test_quantile_dtype_size(self, any_int_ea_dtype):
         result = ser.quantile([0.1, 0.5])
         expected = Series([1, 1], dtype=any_int_ea_dtype, index=[0.1, 0.5])
         tm.assert_series_equal(result, expected)
+
+
+@pytest.mark.parametrize("typ", ["datetime64", "timedelta64"])
+def test_quantile_empty_datetimelike(typ, unit):
+    ser = Series([], dtype=f"{typ}[{unit}]")
+    result = ser.quantile()
+    assert result is pd.NaT