diff --git a/pandas/tests/groupby/test_reductions.py b/pandas/tests/groupby/test_reductions.py
index 3e78e728f5ea9..425079f943aba 100644
--- a/pandas/tests/groupby/test_reductions.py
+++ b/pandas/tests/groupby/test_reductions.py
@@ -1057,3 +1057,27 @@ def test_regression_allowlist_methods(op, axis, skipna, sort):
         if sort:
             expected = expected.sort_index(axis=axis)
         tm.assert_frame_equal(result, expected)
+
+
+def test_groupby_prod_with_int64_dtype():
+    # GH#46573
+    data = [
+        [1, 11],
+        [1, 41],
+        [1, 17],
+        [1, 37],
+        [1, 7],
+        [1, 29],
+        [1, 31],
+        [1, 2],
+        [1, 3],
+        [1, 43],
+        [1, 5],
+        [1, 47],
+        [1, 19],
+        [1, 88],
+    ]
+    df = DataFrame(data, columns=["A", "B"], dtype="int64")
+    result = df.groupby(["A"]).prod().reset_index()
+    expected = DataFrame({"A": [1], "B": [180970905912331920]}, dtype="int64")
+    tm.assert_frame_equal(result, expected)