diff --git a/doc/source/whatsnew/v0.25.0.rst b/doc/source/whatsnew/v0.25.0.rst
index 30ae4ebe21ca4..769713cdf30e5 100644
--- a/doc/source/whatsnew/v0.25.0.rst
+++ b/doc/source/whatsnew/v0.25.0.rst
@@ -774,6 +774,8 @@ Indexing
 - Fixed bug where assigning a :class:`arrays.PandasArray` to a :class:`pandas.core.frame.DataFrame` would raise error (:issue:`26390`)
 - Allow keyword arguments for callable local reference used in the :meth:`DataFrame.query` string (:issue:`26426`)
 - Bug which produced ``AttributeError`` on partial matching :class:`Timestamp` in a :class:`MultiIndex`  (:issue:`26944`)
+- Bug in :meth:`DataFrame.loc` and :meth:`DataFrame.iloc` on a :class:`DataFrame` with a single timezone-aware datetime64[ns] column incorrectly returning a scalar instead of a :class:`Series` (:issue:`27110`)
+-
 
 Missing
 ^^^^^^^
diff --git a/pandas/core/internals/blocks.py b/pandas/core/internals/blocks.py
index b79f87461093d..cad37bf2b8ae1 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -1538,6 +1538,10 @@ def iget(self, col):
             col, loc = col
             if not com.is_null_slice(col) and col != 0:
                 raise IndexError("{0} only contains one item".format(self))
+            elif isinstance(col, slice):
+                if col != slice(None):
+                    raise NotImplementedError(col)
+                return self.values[[loc]]
             return self.values[loc]
         else:
             if col != 0:
diff --git a/pandas/tests/extension/base/getitem.py b/pandas/tests/extension/base/getitem.py
index dfc82c6041eae..6a5507b51b3ba 100644
--- a/pandas/tests/extension/base/getitem.py
+++ b/pandas/tests/extension/base/getitem.py
@@ -73,6 +73,20 @@ def test_loc_frame(self, data):
         result = df.loc[:3, 'A']
         self.assert_series_equal(result, expected)
 
+    def test_loc_iloc_frame_single_dtype(self, data):
+        # GH#27110 bug in ExtensionBlock.iget caused df.iloc[n] to incorrectly
+        #  return a scalar
+        df = pd.DataFrame({"A": data})
+        expected = pd.Series([data[2]], index=["A"], name=2, dtype=data.dtype)
+
+        result = df.loc[2]
+        self.assert_series_equal(result, expected)
+
+        expected = pd.Series([data[-1]], index=["A"], name=len(data) - 1,
+                             dtype=data.dtype)
+        result = df.iloc[-1]
+        self.assert_series_equal(result, expected)
+
     def test_getitem_scalar(self, data):
         result = data[0]
         assert isinstance(result, data.dtype.type)
diff --git a/pandas/tests/extension/test_numpy.py b/pandas/tests/extension/test_numpy.py
index f31fa5b87cfe5..74ca296d23295 100644
--- a/pandas/tests/extension/test_numpy.py
+++ b/pandas/tests/extension/test_numpy.py
@@ -180,6 +180,10 @@ def test_take_series(self, data):
         # ValueError: PandasArray must be 1-dimensional.
         super().test_take_series(data)
 
+    @pytest.mark.xfail(reason="astype doesn't recognize data.dtype")
+    def test_loc_iloc_frame_single_dtype(self, data):
+        super().test_loc_iloc_frame_single_dtype(data)
+
 
 class TestGroupby(BaseNumPyTests, base.BaseGroupbyTests):
     @skip_nested
diff --git a/pandas/tests/groupby/aggregate/test_other.py b/pandas/tests/groupby/aggregate/test_other.py
index a061eaa1a2c6f..903ffa23173cb 100644
--- a/pandas/tests/groupby/aggregate/test_other.py
+++ b/pandas/tests/groupby/aggregate/test_other.py
@@ -421,11 +421,15 @@ def test_agg_timezone_round_trip():
     assert ts == grouped.nth(0)['B'].iloc[0]
     assert ts == grouped.head(1)['B'].iloc[0]
     assert ts == grouped.first()['B'].iloc[0]
-    assert ts == grouped.apply(lambda x: x.iloc[0])[0]
+
+    # GH#27110 applying iloc should return a DataFrame
+    assert ts == grouped.apply(lambda x: x.iloc[0]).iloc[0, 0]
 
     ts = df['B'].iloc[2]
     assert ts == grouped.last()['B'].iloc[0]
-    assert ts == grouped.apply(lambda x: x.iloc[-1])[0]
+
+    # GH#27110 applying iloc should return a DataFrame
+    assert ts == grouped.apply(lambda x: x.iloc[-1]).iloc[0, 0]
 
 
 def test_sum_uint64_overflow():
diff --git a/pandas/tests/indexing/test_datetime.py b/pandas/tests/indexing/test_datetime.py
index d4da34cab6f5c..278fa6bd44f99 100644
--- a/pandas/tests/indexing/test_datetime.py
+++ b/pandas/tests/indexing/test_datetime.py
@@ -39,7 +39,7 @@ def test_setitem_with_datetime_tz(self):
 
     def test_indexing_with_datetime_tz(self):
 
-        # 8260
+        # GH#8260
         # support datetime64 with tz
 
         idx = Index(date_range('20130101', periods=3, tz='US/Eastern'),
@@ -65,11 +65,12 @@ def test_indexing_with_datetime_tz(self):
         # indexing - fast_xs
         df = DataFrame({'a': date_range('2014-01-01', periods=10, tz='UTC')})
         result = df.iloc[5]
-        expected = Timestamp('2014-01-06 00:00:00+0000', tz='UTC', freq='D')
-        assert result == expected
+        expected = Series([Timestamp('2014-01-06 00:00:00+0000', tz='UTC')],
+                          index=['a'], name=5)
+        tm.assert_series_equal(result, expected)
 
         result = df.loc[5]
-        assert result == expected
+        tm.assert_series_equal(result, expected)
 
         # indexing - boolean
         result = df[df.a > df.a[3]]