diff --git a/pandas/tests/util/test_assert_index_equal.py b/pandas/tests/util/test_assert_index_equal.py
index 1fa7b979070a7..0b2c2e12a2d2a 100644
--- a/pandas/tests/util/test_assert_index_equal.py
+++ b/pandas/tests/util/test_assert_index_equal.py
@@ -2,6 +2,7 @@
 import pytest
 
 from pandas import (
+    NA,
     Categorical,
     CategoricalIndex,
     Index,
@@ -238,6 +239,21 @@ def test_index_equal_range_categories(check_categorical, exact):
         )
 
 
+def test_assert_index_equal_different_inferred_types():
+    # GH#31884
+    msg = """\
+Index are different
+
+Attribute "inferred_type" are different
+\\[left\\]:  mixed
+\\[right\\]: datetime"""
+
+    idx1 = Index([NA, np.datetime64("nat")])
+    idx2 = Index([NA, NaT])
+    with pytest.raises(AssertionError, match=msg):
+        tm.assert_index_equal(idx1, idx2)
+
+
 def test_assert_index_equal_different_names_check_order_false():
     # GH#47328
     idx1 = Index([1, 3], name="a")