diff --git a/mypy/stubgen.py b/mypy/stubgen.py
index 1f7a01e6ae3c..ad48f0841b83 100755
--- a/mypy/stubgen.py
+++ b/mypy/stubgen.py
@@ -122,6 +122,7 @@
     generate_guarded,
     infer_method_arg_types,
     infer_method_ret_type,
+    is_private_module,
     remove_misplaced_type_comments,
     report_missing,
     walk_packages,
@@ -1618,6 +1619,9 @@ def generate_stub_for_py_module(
     If directory for target doesn't exist it will created. Existing stub
     will be overwritten.
     """
+    if not include_private and is_private_module(mod.module):
+        return
+
     if inspect:
         ngen = InspectionStubGenerator(
             module_name=mod.module,
diff --git a/mypy/stubutil.py b/mypy/stubutil.py
index 1a9c2357c58e..3e7cc00a0dda 100644
--- a/mypy/stubutil.py
+++ b/mypy/stubutil.py
@@ -805,3 +805,15 @@ def should_reexport(self, name: str, full_module: str, name_is_alias: bool) -> b
         if self._all_:
             return name in self._all_
         return True
+
+
+def is_private_module(module: str) -> bool:
+    """Check if a module is private.
+
+    Return True if at least one module name starts with '_' and does not
+    end with '__'.
+
+    For example, returns True if 'foo._bar.utils' is passed.
+    Returns False if 'foo.bar.__init__' is passed.
+    """
+    return any(name.startswith("_") and not name.endswith("__") for name in module.split("."))