diff --git a/doc/source/whatsnew/v0.24.0.txt b/doc/source/whatsnew/v0.24.0.txt
index 8fe3023e9537c..f143cbd13c22c 100644
--- a/doc/source/whatsnew/v0.24.0.txt
+++ b/doc/source/whatsnew/v0.24.0.txt
@@ -436,6 +436,7 @@ Datetimelike
 
 - Fixed bug where two :class:`DateOffset` objects with different ``normalize`` attributes could evaluate as equal (:issue:`21404`)
 - Fixed bug where :meth:`Timestamp.resolution` incorrectly returned 1-microsecond ``timedelta`` instead of 1-nanosecond :class:`Timedelta` (:issue:`21336`,:issue:`21365`)
+- Fixed bug where :class:`DataFrame` with ``dtype='datetime64[ns]'`` operating with :class:`DateOffset` could cast to ``dtype='object'`` (:issue:`21610`)
 
 Timedelta
 ^^^^^^^^^
diff --git a/pandas/core/internals/__init__.py b/pandas/core/internals/__init__.py
index fde3aaa14ac5d..7ef21784b2d02 100644
--- a/pandas/core/internals/__init__.py
+++ b/pandas/core/internals/__init__.py
@@ -63,7 +63,9 @@
     ABCSeries,
     ABCDatetimeIndex,
     ABCExtensionArray,
-    ABCIndexClass)
+    ABCIndexClass,
+    ABCDateOffset,
+)
 import pandas.core.common as com
 import pandas.core.algorithms as algos
 
@@ -2737,7 +2739,7 @@ def _try_coerce_args(self, values, other):
 
     def _try_coerce_result(self, result):
         """ reverse of try_coerce_args """
-        if isinstance(result, np.ndarray):
+        if isinstance(result, (np.ndarray, Block)):
             if result.dtype.kind in ['i', 'f', 'O']:
                 try:
                     result = result.astype('M8[ns]')
@@ -2785,6 +2787,17 @@ def set(self, locs, values, check=False):
 
         self.values[locs] = values
 
+    def eval(self, func, other, try_cast=False, **kwargs):
+        block = super(DatetimeBlock, self).eval(func, other, try_cast=try_cast,
+                                                **kwargs)[0]
+        if try_cast:
+            if isinstance(other, (np.datetime64, date)):
+                block = TimeDeltaBlock(block.values, block.mgr_locs,
+                                       ndim=block.ndim)
+            elif isinstance(other, ABCDateOffset):
+                block = self._try_coerce_result(block)
+        return [block]
+
 
 class DatetimeTZBlock(NonConsolidatableMixIn, DatetimeBlock):
     """ implement a datetime64 block with a tz attribute """
@@ -2920,6 +2933,8 @@ def _try_coerce_result(self, result):
         if isinstance(result, np.ndarray):
             if result.dtype.kind in ['i', 'f', 'O']:
                 result = result.astype('M8[ns]')
+        elif isinstance(result, Block):
+            result = self.make_block_same_class(result.values.flat)
         elif isinstance(result, (np.integer, np.float, np.datetime64)):
             result = tslibs.Timestamp(result, tz=self.values.tz)
         if isinstance(result, np.ndarray):
diff --git a/pandas/tests/frame/test_arithmetic.py b/pandas/tests/frame/test_arithmetic.py
index fb381a5640519..9a41360f4b7bd 100644
--- a/pandas/tests/frame/test_arithmetic.py
+++ b/pandas/tests/frame/test_arithmetic.py
@@ -1,4 +1,5 @@
 # -*- coding: utf-8 -*-
+import datetime
 import pytest
 import numpy as np
 
@@ -211,6 +212,29 @@ def test_df_sub_datetime64_not_ns(self):
                                  pd.Timedelta(days=2)])
         tm.assert_frame_equal(res, expected)
 
+    def test_timestamp_df_add_dateoffset(self):
+        # GH 21610
+        expected = pd.DataFrame([pd.Timestamp('2019')])
+        result = pd.DataFrame([pd.Timestamp('2018')]) + pd.DateOffset(years=1)
+        tm.assert_frame_equal(expected, result)
+
+        expected = pd.DataFrame([pd.Timestamp('2019', tz='Asia/Shanghai')])
+        result = (pd.DataFrame([pd.Timestamp('2018', tz='Asia/Shanghai')])
+                  + pd.DateOffset(years=1))
+        tm.assert_frame_equal(expected, result)
+
+    @pytest.mark.parametrize('other', [
+        pd.Timestamp('2017'),
+        np.datetime64('2017'),
+        datetime.datetime(2017, 1, 1),
+        datetime.date(2017, 1, 1),
+    ])
+    def test_timestamp_df_sub_timestamp(self, other):
+        # GH 8554 12437
+        expected = pd.DataFrame([pd.Timedelta('365d')])
+        result = pd.DataFrame([pd.Timestamp('2018')]) - other
+        tm.assert_frame_equal(expected, result)
+
     @pytest.mark.parametrize('data', [
         [1, 2, 3],
         [1.1, 2.2, 3.3],
diff --git a/pandas/tests/internals/test_internals.py b/pandas/tests/internals/test_internals.py
index 39418fb72bf4a..f85978e2e3a58 100644
--- a/pandas/tests/internals/test_internals.py
+++ b/pandas/tests/internals/test_internals.py
@@ -1238,7 +1238,6 @@ class TestCanHoldElement(object):
         (2**63, 'complex128'),
         (True, 'bool'),
         (np.timedelta64(20, 'ns'), '<m8[ns]'),
-        (np.datetime64(20, 'ns'), '<M8[ns]'),
     ])
     @pytest.mark.parametrize('op', [
         operator.add,
@@ -1255,7 +1254,6 @@ def test_binop_other(self, op, value, dtype):
                 (operator.truediv, 'bool'),
                 (operator.mod, 'i8'),
                 (operator.mod, 'complex128'),
-                (operator.mod, '<M8[ns]'),
                 (operator.mod, '<m8[ns]'),
                 (operator.pow, 'bool')}
         if (op, dtype) in skip: