diff --git a/doc/source/whatsnew/v1.0.0.rst b/doc/source/whatsnew/v1.0.0.rst
index 8755abe642068..4db4cab9ea91c 100755
--- a/doc/source/whatsnew/v1.0.0.rst
+++ b/doc/source/whatsnew/v1.0.0.rst
@@ -781,6 +781,7 @@ Datetimelike
 - Bug in :class:`Timestamp` subtraction when subtracting a :class:`Timestamp` from a ``np.datetime64`` object incorrectly raising ``TypeError`` (:issue:`28286`)
 - Addition and subtraction of integer or integer-dtype arrays with :class:`Timestamp` will now raise ``NullFrequencyError`` instead of ``ValueError`` (:issue:`28268`)
 - Bug in :class:`Series` and :class:`DataFrame` with integer dtype failing to raise ``TypeError`` when adding or subtracting a ``np.datetime64`` object (:issue:`28080`)
+- Bug in :meth:`Series.astype`, :meth:`Index.astype`, and :meth:`DataFrame.astype` failing to handle ``NaT`` when casting to an integer dtype (:issue:`28492`)
 - Bug in :class:`Week` with ``weekday`` incorrectly raising ``AttributeError`` instead of ``TypeError`` when adding or subtracting an invalid type (:issue:`28530`)
 - Bug in :class:`DataFrame` arithmetic operations when operating with a :class:`Series` with dtype `'timedelta64[ns]'` (:issue:`28049`)
 - Bug in :func:`pandas.core.groupby.generic.SeriesGroupBy.apply` raising ``ValueError`` when a column in the original DataFrame is a datetime and the column labels are not standard integers (:issue:`28247`)
diff --git a/pandas/core/dtypes/cast.py b/pandas/core/dtypes/cast.py
index fa7b45ec4babd..0579c97747bae 100644
--- a/pandas/core/dtypes/cast.py
+++ b/pandas/core/dtypes/cast.py
@@ -823,6 +823,8 @@ def astype_nansafe(arr, dtype, copy: bool = True, skipna: bool = False):
         if is_object_dtype(dtype):
             return tslib.ints_to_pydatetime(arr.view(np.int64))
         elif dtype == np.int64:
+            if isna(arr).any():
+                raise ValueError("Cannot convert NaT values to integer")
             return arr.view(dtype)
 
         # allow frequency conversions
@@ -835,6 +837,8 @@ def astype_nansafe(arr, dtype, copy: bool = True, skipna: bool = False):
         if is_object_dtype(dtype):
             return tslibs.ints_to_pytimedelta(arr.view(np.int64))
         elif dtype == np.int64:
+            if isna(arr).any():
+                raise ValueError("Cannot convert NaT values to integer")
             return arr.view(dtype)
 
         if dtype not in [_INT64_DTYPE, _TD_DTYPE]:
diff --git a/pandas/tests/dtypes/test_common.py b/pandas/tests/dtypes/test_common.py
index 667ee467f2f29..45e41f4bc2228 100644
--- a/pandas/tests/dtypes/test_common.py
+++ b/pandas/tests/dtypes/test_common.py
@@ -5,6 +5,7 @@
 
 import pandas.util._test_decorators as td
 
+from pandas.core.dtypes.cast import astype_nansafe
 import pandas.core.dtypes.common as com
 from pandas.core.dtypes.dtypes import (
     CategoricalDtype,
@@ -13,6 +14,7 @@
     IntervalDtype,
     PeriodDtype,
 )
+from pandas.core.dtypes.missing import isna
 
 import pandas as pd
 from pandas.conftest import (
@@ -721,3 +723,42 @@ def test__get_dtype_fails(input_param, expected_error_message):
 )
 def test__is_dtype_type(input_param, result):
     assert com._is_dtype_type(input_param, lambda tipo: tipo == result)
+
+
+@pytest.mark.parametrize("val", [np.datetime64("NaT"), np.timedelta64("NaT")])
+@pytest.mark.parametrize("typ", [np.int64])
+def test_astype_nansafe(val, typ):
+    arr = np.array([val])
+
+    msg = "Cannot convert NaT values to integer"
+    with pytest.raises(ValueError, match=msg):
+        astype_nansafe(arr, dtype=typ)
+
+
+@pytest.mark.parametrize("from_type", [np.datetime64, np.timedelta64])
+@pytest.mark.parametrize(
+    "to_type",
+    [
+        np.uint8,
+        np.uint16,
+        np.uint32,
+        np.int8,
+        np.int16,
+        np.int32,
+        np.float16,
+        np.float32,
+    ],
+)
+def test_astype_datetime64_bad_dtype_raises(from_type, to_type):
+    arr = np.array([from_type("2018")])
+
+    with pytest.raises(TypeError, match="cannot astype"):
+        astype_nansafe(arr, dtype=to_type)
+
+
+@pytest.mark.parametrize("from_type", [np.datetime64, np.timedelta64])
+def test_astype_object_preserves_datetime_na(from_type):
+    arr = np.array([from_type("NaT")])
+    result = astype_nansafe(arr, dtype="object")
+
+    assert isna(result)[0]