diff --git a/Lib/test/test_traceback.py b/Lib/test/test_traceback.py
index 5dc11253e0d5c8..af7a75bd3cda8d 100644
--- a/Lib/test/test_traceback.py
+++ b/Lib/test/test_traceback.py
@@ -5189,6 +5189,15 @@ def test_no_site_package_flavour(self):
              b"or to enable your virtual environment?"), stderr
         )
 
+        code = """import abs"""
+        _, _, stderr = assert_python_failure('-S', '-c', code)
+        self.assertIn(b"Did you mean: 'abc'?", stderr)
+        self.assertIn(
+            (b"Site initialization is disabled, did you forget to "
+             b"add the site-packages directory to sys.path "
+             b"or to enable your virtual environment?"), stderr
+        )
+
     def test_missing_stdlib_module(self):
         code = """
             import sys
@@ -5266,9 +5275,17 @@ def test_incompatible_extension_modules_hint(self):
                 sys.path.insert(0, {tmp!r})
                 import foo
             '''
-            _, _, stderr = assert_python_failure('-c', code, __cwd=tmp)
+            _, _, stderr1 = assert_python_failure('-c', code, __cwd=tmp)
+            # if used "-S", the message should contain two suggestions
+            _, _, stderr2 = assert_python_failure('-S', '-c', code, __cwd=tmp)
         hint = f'Although a module with this name was found for a different Python version ({incompatible_module}).'
-        self.assertIn(hint, stderr.decode())
+        self.assertIn(hint, stderr1.decode())
+        self.assertIn(hint, stderr2.decode())
+        self.assertIn(
+            (b"Site initialization is disabled, did you forget to "
+             b"add the site-packages directory to sys.path "
+             b"or to enable your virtual environment?"), stderr2
+        )
 
 
 class TestColorizedTraceback(unittest.TestCase):
diff --git a/Lib/traceback.py b/Lib/traceback.py
index 1f9f151ebf5d39..5c13540551c8e7 100644
--- a/Lib/traceback.py
+++ b/Lib/traceback.py
@@ -1125,16 +1125,14 @@ def __init__(self, exc_type, exc_value, exc_traceback, *, limit=None,
                     self._str += f". Did you mean: '{suggestion}' ({suggestion!a})?"
         elif exc_type and issubclass(exc_type, ModuleNotFoundError):
             module_name = getattr(exc_value, "name", None)
+            analyse_sys_no_site = True
             if module_name in sys.stdlib_module_names:
                 message = _MISSING_STDLIB_MODULE_MESSAGES.get(
                     module_name,
                     f"Standard library module {module_name!r} was not found"
                 )
                 self._str = message
-            elif sys.flags.no_site:
-                self._str += (". Site initialization is disabled, did you forget to "
-                    + "add the site-packages directory to sys.path "
-                    + "or to enable your virtual environment?")
+                analyse_sys_no_site = False
             elif abi_tag := _find_incompatible_extension_module(module_name):
                 self._str += (
                     ". Although a module with this name was found for a "
@@ -1144,6 +1142,12 @@ def __init__(self, exc_type, exc_value, exc_traceback, *, limit=None,
                 suggestion = _compute_suggestion_error(exc_value, exc_traceback, module_name)
                 if suggestion:
                     self._str += f". Did you mean: '{suggestion}'?"
+            if analyse_sys_no_site and sys.flags.no_site:
+                if not self._str.endswith((".", "?")):
+                    self._str += "."
+                self._str += (" Site initialization is disabled, did you forget to "
+                    "add the site-packages directory to sys.path "
+                    "or to enable your virtual environment?")
         elif exc_type and issubclass(exc_type, AttributeError) and \
                 getattr(exc_value, "name", None) is not None:
             wrong_name = getattr(exc_value, "name", None)