diff --git a/doc/source/whatsnew/v1.3.2.rst b/doc/source/whatsnew/v1.3.2.rst
index 7a9549affef00..e3c6268547dd2 100644
--- a/doc/source/whatsnew/v1.3.2.rst
+++ b/doc/source/whatsnew/v1.3.2.rst
@@ -26,6 +26,7 @@ Fixed regressions
 - Fixed regression in :func:`concat` where ``copy=False`` was not honored in ``axis=1`` Series concatenation (:issue:`42501`)
 - Regression in :meth:`Series.nlargest` and :meth:`Series.nsmallest` with nullable integer or float dtype (:issue:`42816`)
 - Fixed regression in :meth:`Series.quantile` with :class:`Int64Dtype` (:issue:`42626`)
+- Fixed regression in :meth:`Series.groupby` and :meth:`DataFrame.groupby` where supplying the ``by`` argument with a Series named with a tuple would incorrectly raise (:issue:`42731`)
 
 .. ---------------------------------------------------------------------------
 
diff --git a/pandas/core/groupby/grouper.py b/pandas/core/groupby/grouper.py
index 260416576d79e..c79dadcadc8cd 100644
--- a/pandas/core/groupby/grouper.py
+++ b/pandas/core/groupby/grouper.py
@@ -845,9 +845,11 @@ def is_in_obj(gpr) -> bool:
             return False
         try:
             return gpr is obj[gpr.name]
-        except (KeyError, IndexError):
+        except (KeyError, IndexError, InvalidIndexError):
             # IndexError reached in e.g. test_skip_group_keys when we pass
             #  lambda here
+            # InvalidIndexError raised on key-types inappropriate for index,
+            #  e.g. DatetimeIndex.get_loc(tuple())
             return False
 
     for gpr, level in zip(keys, levels):
diff --git a/pandas/tests/groupby/test_grouping.py b/pandas/tests/groupby/test_grouping.py
index 1d2f1c7a49759..527b93a28359c 100644
--- a/pandas/tests/groupby/test_grouping.py
+++ b/pandas/tests/groupby/test_grouping.py
@@ -400,6 +400,23 @@ def test_groupby_dict_mapping(self):
         tm.assert_series_equal(result, result2)
         tm.assert_series_equal(result, expected2)
 
+    @pytest.mark.parametrize(
+        "index",
+        [
+            [0, 1, 2, 3],
+            ["a", "b", "c", "d"],
+            [Timestamp(2021, 7, 28 + i) for i in range(4)],
+        ],
+    )
+    def test_groupby_series_named_with_tuple(self, frame_or_series, index):
+        # GH 42731
+        obj = frame_or_series([1, 2, 3, 4], index=index)
+        groups = Series([1, 0, 1, 0], index=index, name=("a", "a"))
+        result = obj.groupby(groups).last()
+        expected = frame_or_series([4, 3])
+        expected.index.name = ("a", "a")
+        tm.assert_equal(result, expected)
+
     def test_groupby_grouper_f_sanity_checked(self):
         dates = date_range("01-Jan-2013", periods=12, freq="MS")
         ts = Series(np.random.randn(12), index=dates)