diff --git a/pandas/core/reshape/util.py b/pandas/core/reshape/util.py
index a1bf3f8ee4119..d2c08712abacd 100644
--- a/pandas/core/reshape/util.py
+++ b/pandas/core/reshape/util.py
@@ -39,6 +39,9 @@ def cartesian_product(X):
     lenX = np.fromiter((len(x) for x in X), dtype=np.intp)
     cumprodX = np.cumproduct(lenX)
 
+    if np.any(cumprodX < 0):
+        raise ValueError("Product space too large to allocate arrays!")
+
     a = np.roll(cumprodX, 1)
     a[0] = 1
 
diff --git a/pandas/tests/reshape/test_util.py b/pandas/tests/reshape/test_util.py
index 9d074b5ade425..0acadc54cec0c 100644
--- a/pandas/tests/reshape/test_util.py
+++ b/pandas/tests/reshape/test_util.py
@@ -65,3 +65,13 @@ def test_invalid_input(self, X):
 
         with pytest.raises(TypeError, match=msg):
             cartesian_product(X=X)
+
+    def test_exceed_product_space(self):
+        # GH31355: raise useful error when produce space is too large
+        msg = "Product space too large to allocate arrays!"
+
+        with pytest.raises(ValueError, match=msg):
+            dims = [np.arange(0, 22, dtype=np.int16) for i in range(12)] + [
+                (np.arange(15128, dtype=np.int16)),
+            ]
+            cartesian_product(X=dims)