diff --git a/mypy/modulefinder.py b/mypy/modulefinder.py
index b2abb4847705..265d76ed5bb6 100644
--- a/mypy/modulefinder.py
+++ b/mypy/modulefinder.py
@@ -507,7 +507,11 @@ def _find_module(self, id: str, use_typeshed: bool) -> ModuleSearchResult:
 
             # In namespace mode, register a potential namespace package
             if self.options and self.options.namespace_packages:
-                if fscache.exists_case(base_path, dir_prefix) and not has_init:
+                if (
+                    not has_init
+                    and fscache.exists_case(base_path, dir_prefix)
+                    and not fscache.isfile_case(base_path, dir_prefix)
+                ):
                     near_misses.append((base_path, dir_prefix))
 
             # No package, look for module.
diff --git a/test-data/packages/modulefinder/nsx-pkg3/nsx/c/c b/test-data/packages/modulefinder/nsx-pkg3/nsx/c/c
new file mode 100644
index 000000000000..e69de29bb2d1
diff --git a/test-data/packages/modulefinder/pkg1/a b/test-data/packages/modulefinder/pkg1/a
new file mode 100644
index 000000000000..e69de29bb2d1