diff --git a/pandas/tests/groupby/test_quantile.py b/pandas/tests/groupby/test_quantile.py
index 20328426a69b2..2b7e71d9619a4 100644
--- a/pandas/tests/groupby/test_quantile.py
+++ b/pandas/tests/groupby/test_quantile.py
@@ -343,3 +343,38 @@ def test_columns_groupby_quantile():
     )
 
     tm.assert_frame_equal(result, expected)
+
+
+def test_timestamp_groupby_quantile():
+    # GH 33168
+    df = DataFrame(
+        {
+            "timestamp": pd.date_range(
+                start="2020-04-19 00:00:00", freq="1T", periods=100, tz="UTC"
+            ).floor("1H"),
+            "category": list(range(1, 101)),
+            "value": list(range(101, 201)),
+        }
+    )
+
+    result = df.groupby("timestamp").quantile([0.2, 0.8])
+
+    expected = DataFrame(
+        [
+            {"category": 12.8, "value": 112.8},
+            {"category": 48.2, "value": 148.2},
+            {"category": 68.8, "value": 168.8},
+            {"category": 92.2, "value": 192.2},
+        ],
+        index=pd.MultiIndex.from_tuples(
+            [
+                (pd.Timestamp("2020-04-19 00:00:00+00:00"), 0.2),
+                (pd.Timestamp("2020-04-19 00:00:00+00:00"), 0.8),
+                (pd.Timestamp("2020-04-19 01:00:00+00:00"), 0.2),
+                (pd.Timestamp("2020-04-19 01:00:00+00:00"), 0.8),
+            ],
+            names=("timestamp", None),
+        ),
+    )
+
+    tm.assert_frame_equal(result, expected)