diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index 3b60085e9fa66..818a0cccae184 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -816,6 +816,7 @@ Groupby/resample/rolling
 - Bug in :meth:`DataFrame.groupby` where a ``ValueError`` would be raised when grouping by a categorical column with read-only categories and ``sort=False`` (:issue:`33410`)
 - Bug in :meth:`GroupBy.first` and :meth:`GroupBy.last` where None is not preserved in object dtype (:issue:`32800`)
 - Bug in :meth:`Rolling.min` and :meth:`Rolling.max`: Growing memory usage after multiple calls when using a fixed window (:issue:`30726`)
+- Bug in :meth:`Series.groupby` would raise ``ValueError`` when grouping by :class:`PeriodIndex` level (:issue:`34010`)
 - Bug in :meth:`GroupBy.agg`, :meth:`GroupBy.transform`, and :meth:`GroupBy.resample` where subclasses are not preserved (:issue:`28330`)
 - Bug in :meth:`GroupBy.rolling.apply` ignores args and kwargs parameters (:issue:`33433`)
 
diff --git a/pandas/core/groupby/grouper.py b/pandas/core/groupby/grouper.py
index 9660fb9c2e1b0..39892d87bfd69 100644
--- a/pandas/core/groupby/grouper.py
+++ b/pandas/core/groupby/grouper.py
@@ -754,7 +754,9 @@ def is_in_obj(gpr) -> bool:
             return False
         try:
             return gpr is obj[gpr.name]
-        except (KeyError, IndexError):
+        except (KeyError, IndexError, ValueError):
+            # TODO: ValueError: Given date string not likely a datetime.
+            # should be KeyError?
             return False
 
     for i, (gpr, level) in enumerate(zip(keys, levels)):
diff --git a/pandas/tests/groupby/test_size.py b/pandas/tests/groupby/test_size.py
index 346e6ae6cb9cb..42bccc67fe0f8 100644
--- a/pandas/tests/groupby/test_size.py
+++ b/pandas/tests/groupby/test_size.py
@@ -1,7 +1,7 @@
 import numpy as np
 import pytest
 
-from pandas import DataFrame, Index, Series
+from pandas import DataFrame, Index, PeriodIndex, Series
 import pandas._testing as tm
 
 
@@ -36,3 +36,11 @@ def test_size_groupby_all_null():
     result = df.groupby("A").size()
     expected = Series(dtype="int64", index=Index([], name="A"))
     tm.assert_series_equal(result, expected)
+
+
+def test_size_period_index():
+    # https://github.com/pandas-dev/pandas/issues/34010
+    ser = Series([1], index=PeriodIndex(["2000"], name="A", freq="D"))
+    grp = ser.groupby(level="A")
+    result = grp.size()
+    tm.assert_series_equal(result, ser)