diff --git a/Lib/inspect.py b/Lib/inspect.py
index 531b891283b5334..6d43d8dad46b997 100644
--- a/Lib/inspect.py
+++ b/Lib/inspect.py
@@ -859,7 +859,7 @@ def getmodule(object, _filename=None):
     # Try the cache again with the absolute file name
     try:
         file = getabsfile(object, _filename)
-    except TypeError:
+    except (TypeError, FileNotFoundError):
         return None
     if file in modulesbyfile:
         return sys.modules.get(modulesbyfile[file])
diff --git a/Lib/test/test_inspect.py b/Lib/test/test_inspect.py
index 4164634417b2ade..93ff2f85df193d0 100644
--- a/Lib/test/test_inspect.py
+++ b/Lib/test/test_inspect.py
@@ -493,6 +493,15 @@ def test_getmodule(self):
         # Check filename override
         self.assertEqual(inspect.getmodule(None, modfile), mod)
 
+    def test_getmodule_file_not_found(self):
+        # See bpo-45406
+        def _getabsfile(obj, _filename):
+            raise FileNotFoundError('bad file')
+        with unittest.mock.patch('inspect.getabsfile', _getabsfile):
+            f = inspect.currentframe()
+            self.assertIsNone(inspect.getmodule(f))
+            inspect.getouterframes(f)  # smoke test
+
     def test_getframeinfo_get_first_line(self):
         frame_info = inspect.getframeinfo(self.fodderModule.fr, 50)
         self.assertEqual(frame_info.code_context[0], "# line 1\n")
diff --git a/Misc/NEWS.d/next/Library/2021-10-08-19-24-48.bpo-45406.Qh_Mz4.rst b/Misc/NEWS.d/next/Library/2021-10-08-19-24-48.bpo-45406.Qh_Mz4.rst
new file mode 100644
index 000000000000000..2c3a8165aeb492e
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2021-10-08-19-24-48.bpo-45406.Qh_Mz4.rst
@@ -0,0 +1 @@
+Make :func:`inspect.getmodule` catch ``FileNotFoundError`` raised by  :'func:`inspect.getabsfile`, and return ``None`` to indicate that the module could not be determined.
\ No newline at end of file