diff --git a/mypy/modulefinder.py b/mypy/modulefinder.py
index fee484ae02fb..5adb7c059e07 100644
--- a/mypy/modulefinder.py
+++ b/mypy/modulefinder.py
@@ -553,7 +553,11 @@ def _find_module(self, id: str, use_typeshed: bool) -> ModuleSearchResult:
             return ancestor
 
         if approved_stub_package_exists(id):
-            return ModuleNotFoundReason.APPROVED_STUBS_NOT_INSTALLED
+            if len(components) == 1 or (
+                self.find_module(components[0])
+                is ModuleNotFoundReason.APPROVED_STUBS_NOT_INSTALLED
+            ):
+                return ModuleNotFoundReason.APPROVED_STUBS_NOT_INSTALLED
         elif found_possible_third_party_missing_type_hints:
             return ModuleNotFoundReason.FOUND_WITHOUT_TYPE_HINTS
         else: