diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index a593a03de5c25..43756082a7442 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -543,7 +543,7 @@ Datetimelike
 Timedelta
 ^^^^^^^^^
 - Bug in division of all-``NaT`` :class:`TimeDeltaIndex`, :class:`Series` or :class:`DataFrame` column with object-dtype arraylike of numbers failing to infer the result as timedelta64-dtype (:issue:`39750`)
--
+- Bug in floor division of ``timedelta64[ns]`` data with a scalar returning garbage values (:issue:`44466`)
 
 Timezones
 ^^^^^^^^^
diff --git a/pandas/core/arrays/timedeltas.py b/pandas/core/arrays/timedeltas.py
index 3d8f9f7edcc74..91e90ebdb6253 100644
--- a/pandas/core/arrays/timedeltas.py
+++ b/pandas/core/arrays/timedeltas.py
@@ -651,8 +651,7 @@ def __floordiv__(self, other):
 
             # at this point we should only have numeric scalars; anything
             #  else will raise
-            result = self.asi8 // other
-            np.putmask(result, self._isnan, iNaT)
+            result = self._ndarray / other
             freq = None
             if self.freq is not None:
                 # Note: freq gets division, not floor-division
@@ -661,7 +660,7 @@ def __floordiv__(self, other):
                     # e.g. if self.freq is Nano(1) then dividing by 2
                     #  rounds down to zero
                     freq = None
-            return type(self)(result.view("m8[ns]"), freq=freq)
+            return type(self)(result, freq=freq)
 
         if not hasattr(other, "dtype"):
             # list, tuple
diff --git a/pandas/tests/arithmetic/test_timedelta64.py b/pandas/tests/arithmetic/test_timedelta64.py
index 8078e8c90a2bf..93332b9b96f84 100644
--- a/pandas/tests/arithmetic/test_timedelta64.py
+++ b/pandas/tests/arithmetic/test_timedelta64.py
@@ -1981,6 +1981,20 @@ def test_td64arr_div_numeric_scalar(self, box_with_array, two):
         with pytest.raises(TypeError, match="Cannot divide"):
             two / tdser
 
+    @pytest.mark.parametrize("two", [2, 2.0, np.array(2), np.array(2.0)])
+    def test_td64arr_floordiv_numeric_scalar(self, box_with_array, two):
+        tdser = Series(["59 Days", "59 Days", "NaT"], dtype="m8[ns]")
+        expected = Series(["29.5D", "29.5D", "NaT"], dtype="timedelta64[ns]")
+
+        tdser = tm.box_expected(tdser, box_with_array)
+        expected = tm.box_expected(expected, box_with_array)
+
+        result = tdser // two
+        tm.assert_equal(result, expected)
+
+        with pytest.raises(TypeError, match="Cannot divide"):
+            two // tdser
+
     @pytest.mark.parametrize(
         "vector",
         [np.array([20, 30, 40]), pd.Index([20, 30, 40]), Series([20, 30, 40])],