diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index 5bffc4ec552af..d30765217390f 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -3243,9 +3243,13 @@ def union(self, other, sort=None):
 
         # TODO: Index.union returns other when `len(self)` is 0.
 
-        uniq_tuples = lib.fast_unique_multiple(
-            [self._values, other._ndarray_values], sort=sort
-        )
+        if not is_object_dtype(other.dtype):
+            raise NotImplementedError(
+                "Can only union MultiIndex with MultiIndex or Index of tuples, "
+                "try mi.to_flat_index().union(other) instead."
+            )
+
+        uniq_tuples = lib.fast_unique_multiple([self._values, other._values], sort=sort)
 
         return MultiIndex.from_arrays(
             zip(*uniq_tuples), sortorder=0, names=result_names
@@ -3279,8 +3283,18 @@ def intersection(self, other, sort=False):
         if self.equals(other):
             return self
 
+        if not is_object_dtype(other.dtype):
+            # The intersection is empty
+            # TODO: we have no tests that get here
+            return MultiIndex(
+                levels=self.levels,
+                codes=[[]] * self.nlevels,
+                names=result_names,
+                verify_integrity=False,
+            )
+
         lvals = self._values
-        rvals = other._ndarray_values
+        rvals = other._values
 
         uniq_tuples = None  # flag whether _inner_indexer was succesful
         if self.is_monotonic and other.is_monotonic:
diff --git a/pandas/tests/indexes/multi/test_setops.py b/pandas/tests/indexes/multi/test_setops.py
index d7d0ff4c411aa..b24f56afee376 100644
--- a/pandas/tests/indexes/multi/test_setops.py
+++ b/pandas/tests/indexes/multi/test_setops.py
@@ -246,6 +246,7 @@ def test_union(idx, sort):
     the_union = idx.union(idx[:0], sort=sort)
     assert the_union is idx
 
+    # FIXME: dont leave commented-out
     # won't work in python 3
     # tuples = _index.values
     # result = _index[:4] | tuples[4:]
@@ -282,6 +283,7 @@ def test_intersection(idx, sort):
     expected = idx[:0]
     assert empty.equals(expected)
 
+    # FIXME: dont leave commented-out
     # can't do in python 3
     # tuples = _index.values
     # result = _index & tuples
@@ -351,6 +353,17 @@ def test_union_sort_other_incomparable_sort():
         idx.union(idx[:1], sort=True)
 
 
+def test_union_non_object_dtype_raises():
+    # GH#32646 raise NotImplementedError instead of less-informative error
+    mi = pd.MultiIndex.from_product([["a", "b"], [1, 2]])
+
+    idx = mi.levels[1]
+
+    msg = "Can only union MultiIndex with MultiIndex or Index of tuples"
+    with pytest.raises(NotImplementedError, match=msg):
+        mi.union(idx)
+
+
 @pytest.mark.parametrize(
     "method", ["union", "intersection", "difference", "symmetric_difference"]
 )