diff --git a/doc/source/whatsnew/v0.23.0.txt b/doc/source/whatsnew/v0.23.0.txt
index 4c1e98b236db7..86661eb5e4414 100644
--- a/doc/source/whatsnew/v0.23.0.txt
+++ b/doc/source/whatsnew/v0.23.0.txt
@@ -896,6 +896,7 @@ Reshaping
 - Bug in :func:`DataFrame.join` which does an ``outer`` instead of a ``left`` join when being called with multiple DataFrames and some have non-unique indices (:issue:`19624`)
 - :func:`Series.rename` now accepts ``axis`` as a kwarg (:issue:`18589`)
 - Comparisons between :class:`Series` and :class:`Index` would return a ``Series`` with an incorrect name, ignoring the ``Index``'s name attribute (:issue:`19582`)
+- Bug in :func:`qcut` where datetime and timedelta data with ``NaT`` present raised a ``ValueError`` (:issue:`19768`)
 
 Other
 ^^^^^
diff --git a/pandas/core/reshape/tile.py b/pandas/core/reshape/tile.py
index 777f08bd9db2b..359c030157bd3 100644
--- a/pandas/core/reshape/tile.py
+++ b/pandas/core/reshape/tile.py
@@ -279,18 +279,22 @@ def _trim_zeros(x):
 def _coerce_to_type(x):
     """
     if the passed data is of datetime/timedelta type,
-    this method converts it to integer so that cut method can
+    this method converts it to numeric so that cut method can
     handle it
     """
     dtype = None
 
     if is_timedelta64_dtype(x):
-        x = to_timedelta(x).view(np.int64)
+        x = to_timedelta(x)
         dtype = np.timedelta64
     elif is_datetime64_dtype(x):
-        x = to_datetime(x).view(np.int64)
+        x = to_datetime(x)
         dtype = np.datetime64
 
+    if dtype is not None:
+        # GH 19768: force NaT to NaN during integer conversion
+        x = np.where(x.notna(), x.view(np.int64), np.nan)
+
     return x, dtype
 
 
diff --git a/pandas/tests/reshape/test_tile.py b/pandas/tests/reshape/test_tile.py
index f7262a2f0da63..ff914273d47b1 100644
--- a/pandas/tests/reshape/test_tile.py
+++ b/pandas/tests/reshape/test_tile.py
@@ -6,7 +6,8 @@
 
 from pandas import (Series, isna, to_datetime, DatetimeIndex,
                     Timestamp, Interval, IntervalIndex, Categorical,
-                    cut, qcut, date_range)
+                    cut, qcut, date_range, NaT, TimedeltaIndex)
+from pandas.tseries.offsets import Nano, Day
 import pandas.util.testing as tm
 from pandas.api.types import CategoricalDtype as CDT
 
@@ -250,6 +251,18 @@ def test_qcut_nas(self):
         result = qcut(arr, 4)
         assert isna(result[:20]).all()
 
+    @pytest.mark.parametrize('s', [
+        Series(DatetimeIndex(['20180101', NaT, '20180103'])),
+        Series(TimedeltaIndex(['0 days', NaT, '2 days']))],
+        ids=lambda x: str(x.dtype))
+    def test_qcut_nat(self, s):
+        # GH 19768
+        intervals = IntervalIndex.from_tuples(
+            [(s[0] - Nano(), s[2] - Day()), np.nan, (s[2] - Day(), s[2])])
+        expected = Series(Categorical(intervals, ordered=True))
+        result = qcut(s, 2)
+        tm.assert_series_equal(result, expected)
+
     def test_qcut_index(self):
         result = qcut([0, 2], 2)
         intervals = [Interval(-0.001, 1), Interval(1, 2)]