diff --git a/django/contrib/postgres/fields/array.py b/django/contrib/postgres/fields/array.py
index 3edc72ac94..c247387eb7 100644
--- a/django/contrib/postgres/fields/array.py
+++ b/django/contrib/postgres/fields/array.py
@@ -237,7 +237,9 @@ class ArrayField(CheckFieldDefaultMixin, Field):
 
 class ArrayRHSMixin:
     def __init__(self, lhs, rhs):
-        if isinstance(rhs, (tuple, list)):
+        # Don't wrap arrays that contains only None values, psycopg2 doesn't
+        # allow this.
+        if isinstance(rhs, (tuple, list)) and any(self._rhs_not_none_values(rhs)):
             expressions = []
             for value in rhs:
                 if not hasattr(value, "resolve_expression"):
@@ -256,6 +258,13 @@ class ArrayRHSMixin:
         cast_type = self.lhs.output_field.cast_db_type(connection)
         return "%s::%s" % (rhs, cast_type), rhs_params
 
+    def _rhs_not_none_values(self, rhs):
+        for x in rhs:
+            if isinstance(x, (list, tuple)):
+                yield from self._rhs_not_none_values(x)
+            elif x is not None:
+                yield True
+
 
 @ArrayField.register_lookup
 class ArrayContains(ArrayRHSMixin, lookups.DataContains):
diff --git a/tests/postgres_tests/test_array.py b/tests/postgres_tests/test_array.py
index fc4687b68c..89603e24a0 100644
--- a/tests/postgres_tests/test_array.py
+++ b/tests/postgres_tests/test_array.py
@@ -253,6 +253,24 @@ class TestQuerying(PostgreSQLTestCase):
             [obj],
         )
 
+    def test_exact_null_only_nested_array(self):
+        obj1 = NullableIntegerArrayModel.objects.create(field_nested=[[None, None]])
+        obj2 = NullableIntegerArrayModel.objects.create(
+            field_nested=[[None, None], [None, None]],
+        )
+        self.assertSequenceEqual(
+            NullableIntegerArrayModel.objects.filter(
+                field_nested__exact=[[None, None]],
+            ),
+            [obj1],
+        )
+        self.assertSequenceEqual(
+            NullableIntegerArrayModel.objects.filter(
+                field_nested__exact=[[None, None], [None, None]],
+            ),
+            [obj2],
+        )
+
     def test_exact_with_expression(self):
         self.assertSequenceEqual(
             NullableIntegerArrayModel.objects.filter(field__exact=[Value(1)]),