diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index b16ca0a80c5b4..0cb316a829c8c 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -64,7 +64,7 @@ Datetimelike
 
 Timedelta
 ^^^^^^^^^
-
+- Bug in :class:`TimedeltaIndex`, :class:`Series`, and :class:`DataFrame` floor-division with ``timedelta64`` dtypes and ``NaT`` in the denominator (:issue:`35529`)
 -
 -
 
diff --git a/pandas/core/arrays/timedeltas.py b/pandas/core/arrays/timedeltas.py
index a378423df788b..99a4725c2d806 100644
--- a/pandas/core/arrays/timedeltas.py
+++ b/pandas/core/arrays/timedeltas.py
@@ -628,7 +628,7 @@ def __floordiv__(self, other):
             result = self.asi8 // other.asi8
             mask = self._isnan | other._isnan
             if mask.any():
-                result = result.astype(np.int64)
+                result = result.astype(np.float64)
                 result[mask] = np.nan
             return result
 
diff --git a/pandas/tests/arithmetic/test_timedelta64.py b/pandas/tests/arithmetic/test_timedelta64.py
index f94408d657ae5..64d3d5b6d684d 100644
--- a/pandas/tests/arithmetic/test_timedelta64.py
+++ b/pandas/tests/arithmetic/test_timedelta64.py
@@ -1733,6 +1733,23 @@ def test_tdarr_div_length_mismatch(self, box_with_array):
     # ------------------------------------------------------------------
     # __floordiv__, __rfloordiv__
 
+    def test_td64arr_floordiv_td64arr_with_nat(self, box_with_array):
+        # GH#35529
+        box = box_with_array
+
+        left = pd.Series([1000, 222330, 30], dtype="timedelta64[ns]")
+        right = pd.Series([1000, 222330, None], dtype="timedelta64[ns]")
+
+        left = tm.box_expected(left, box)
+        right = tm.box_expected(right, box)
+
+        expected = np.array([1.0, 1.0, np.nan], dtype=np.float64)
+        expected = tm.box_expected(expected, box)
+
+        result = left // right
+
+        tm.assert_equal(result, expected)
+
     def test_td64arr_floordiv_tdscalar(self, box_with_array, scalar_td):
         # GH#18831
         td1 = Series([timedelta(minutes=5, seconds=3)] * 3)