diff --git a/django/db/models/query.py b/django/db/models/query.py
index 1bc8e2ed2ae..661ebd1f247 100644
--- a/django/db/models/query.py
+++ b/django/db/models/query.py
@@ -325,6 +325,7 @@ class QuerySet:
         return cls
 
     def __and__(self, other):
+        self._check_operator_queryset(other, '&')
         self._merge_sanity_check(other)
         if isinstance(other, EmptyQuerySet):
             return other
@@ -336,6 +337,7 @@ class QuerySet:
         return combined
 
     def __or__(self, other):
+        self._check_operator_queryset(other, '|')
         self._merge_sanity_check(other)
         if isinstance(self, EmptyQuerySet):
             return other
@@ -1430,6 +1432,10 @@ class QuerySet:
                 % (operation_name, self.query.combinator)
             )
 
+    def _check_operator_queryset(self, other, operator_):
+        if self.query.combinator or other.query.combinator:
+            raise TypeError(f'Cannot use {operator_} operator with combined queryset.')
+
 
 class InstanceCheckMeta(type):
     def __instancecheck__(self, instance):
diff --git a/tests/queries/test_qs_combinators.py b/tests/queries/test_qs_combinators.py
index 351a4019025..89d08ef6db9 100644
--- a/tests/queries/test_qs_combinators.py
+++ b/tests/queries/test_qs_combinators.py
@@ -441,3 +441,24 @@ class QuerySetSetOperationTests(TestCase):
             with self.subTest(combinator=combinator):
                 with self.assertRaisesMessage(NotSupportedError, msg % combinator):
                     getattr(qs, combinator)(qs).get(num=2)
+
+    def test_operator_on_combined_qs_error(self):
+        qs = Number.objects.all()
+        msg = 'Cannot use %s operator with combined queryset.'
+        combinators = ['union']
+        if connection.features.supports_select_difference:
+            combinators.append('difference')
+        if connection.features.supports_select_intersection:
+            combinators.append('intersection')
+        operators = [
+            ('|', operator.or_),
+            ('&', operator.and_),
+        ]
+        for combinator in combinators:
+            combined_qs = getattr(qs, combinator)(qs)
+            for operator_, operator_func in operators:
+                with self.subTest(combinator=combinator):
+                    with self.assertRaisesMessage(TypeError, msg % operator_):
+                        operator_func(qs, combined_qs)
+                    with self.assertRaisesMessage(TypeError, msg % operator_):
+                        operator_func(combined_qs, qs)