diff --git a/coverage/inorout.py b/coverage/inorout.py
index d5e8b2269..17e11b64a 100644
--- a/coverage/inorout.py
+++ b/coverage/inorout.py
@@ -359,6 +359,10 @@ def warn_already_imported_files(self):
                 if filename in warned:
                     continue
 
+                if len(getattr(mod, "__path__", ())) > 1:
+                    # A namespace package, which confuses this code, so ignore it.
+                    continue
+
                 disp = self.should_trace(filename)
                 if disp.trace:
                     msg = "Already imported a file that will be measured: {}".format(filename)