diff --git a/pandas/tests/indexing/multiindex/test_multiindex.py b/pandas/tests/indexing/multiindex/test_multiindex.py
index 193f3eb1a590f..08e15545cb998 100644
--- a/pandas/tests/indexing/multiindex/test_multiindex.py
+++ b/pandas/tests/indexing/multiindex/test_multiindex.py
@@ -214,6 +214,11 @@ def test_subtracting_two_series_with_unordered_index_and_all_nan_index(
         tm.assert_series_equal(result[0], a_series_expected)
         tm.assert_series_equal(result[1], b_series_expected)
 
+    def test_nunique_smoke(self):
+        # GH 34019
+        n = DataFrame([[1, 2], [1, 2]]).set_index([0, 1]).index.nunique()
+        assert n == 1
+
     def test_multiindex_repeated_keys(self):
         # GH19414
         tm.assert_series_equal(