diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index 407e8ba029ada..fca7e7d209031 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -256,6 +256,7 @@ Groupby/resample/rolling
 - Bug in :meth:`DataFrameGroupBy.apply` where a non-nuisance grouping column would be dropped from the output columns if another groupby method was called before ``.apply()`` (:issue:`34656`)
 - Bug in :meth:`DataFrameGroupby.apply` would drop a :class:`CategoricalIndex` when grouped on. (:issue:`35792`)
 - Bug when subsetting columns on a :class:`~pandas.core.groupby.DataFrameGroupBy` (e.g. ``df.groupby('a')[['b']])``) would reset the attributes ``axis``, ``dropna``, ``group_keys``, ``level``, ``mutated``, ``sort``, and ``squeeze`` to their default values. (:issue:`9959`)
+- Bug in :meth:`DataFrameGroupby.tshift` failing to raise ``ValueError`` when a frequency cannot be inferred for the index of a group (:issue:`35937`)
 -
 
 Reshaping
diff --git a/pandas/_libs/reduction.pyx b/pandas/_libs/reduction.pyx
index 7b36bc8baf891..8161b5c5c2b11 100644
--- a/pandas/_libs/reduction.pyx
+++ b/pandas/_libs/reduction.pyx
@@ -53,6 +53,7 @@ cdef class _BaseGrouper:
             # to a 1-d ndarray like datetime / timedelta / period.
             object.__setattr__(cached_ityp, '_index_data', islider.buf)
             cached_ityp._engine.clear_mapping()
+            cached_ityp._cache.clear()  # e.g. inferred_freq must go
             object.__setattr__(cached_typ._mgr._block, 'values', vslider.buf)
             object.__setattr__(cached_typ._mgr._block, 'mgr_locs',
                                slice(len(vslider.buf)))
@@ -71,6 +72,7 @@ cdef class _BaseGrouper:
             object res
 
         cached_ityp._engine.clear_mapping()
+        cached_ityp._cache.clear()  # e.g. inferred_freq must go
         res = self.f(cached_typ)
         res = _extract_result(res)
         if not initialized:
@@ -455,6 +457,7 @@ cdef class BlockSlider:
 
         object.__setattr__(self.index, '_index_data', self.idx_slider.buf)
         self.index._engine.clear_mapping()
+        self.index._cache.clear()  # e.g. inferred_freq must go
 
     cdef reset(self):
         cdef:
diff --git a/pandas/tests/groupby/test_allowlist.py b/pandas/tests/groupby/test_allowlist.py
index 0fd66cc047017..4a735fc7bb686 100644
--- a/pandas/tests/groupby/test_allowlist.py
+++ b/pandas/tests/groupby/test_allowlist.py
@@ -369,7 +369,6 @@ def test_groupby_selection_with_methods(df):
         "ffill",
         "bfill",
         "pct_change",
-        "tshift",
     ]
 
     for m in methods:
@@ -379,6 +378,11 @@ def test_groupby_selection_with_methods(df):
         # should always be frames!
         tm.assert_frame_equal(res, exp)
 
+    # check that the index cache is cleared
+    with pytest.raises(ValueError, match="Freq was not set in the index"):
+        # GH#35937
+        g.tshift()
+
     # methods which aren't just .foo()
     tm.assert_frame_equal(g.fillna(0), g_exp.fillna(0))
     tm.assert_frame_equal(g.dtypes, g_exp.dtypes)