diff --git a/Orange/widgets/unsupervised/owdistancefile.py b/Orange/widgets/unsupervised/owdistancefile.py
index bed14aada18..c851f90656a 100644
--- a/Orange/widgets/unsupervised/owdistancefile.py
+++ b/Orange/widgets/unsupervised/owdistancefile.py
@@ -124,6 +124,8 @@ def open_file(self):
                 err = str(exc)
                 self.Error.invalid_file(" \n"[len(err) > 40] + err)
             else:
+                # If you add any other checks before accepting the file,
+                # you should probably mirror them in canDropFile
                 if distances.shape[0] != distances.shape[1]:
                     self.Error.non_square_matrix()
                 else:
@@ -158,7 +160,12 @@ def parametersFromFile(self, path):
         return {"recent_paths": stored_recent_paths_prepend(self.WIDGET, r)}
 
     def canDropFile(self, path: str) -> bool:
-        return os.path.splitext(path)[1].lower() in (".dst", ".xlsx")
+        try:
+            distances = DistMatrix.from_file(path)
+        except Exception:  # pylint: disable=broad-except
+            return False
+        else:
+            return distances.shape[0] == distances.shape[1]
 
 
 if __name__ == "__main__":  # pragma: no cover
diff --git a/Orange/widgets/unsupervised/tests/test_owdistancefile.py b/Orange/widgets/unsupervised/tests/test_owdistancefile.py
index 9e6232d3e1c..0defa82a487 100644
--- a/Orange/widgets/unsupervised/tests/test_owdistancefile.py
+++ b/Orange/widgets/unsupervised/tests/test_owdistancefile.py
@@ -35,9 +35,13 @@ def test_nan_to_num(self):
 
 class TestOWDistanceFileDropHandler(unittest.TestCase):
     def test_canDropFile(self):
+        def fn(name):
+            return os.path.join(os.path.split(Orange.tests.__file__)[0], name)
+
         handler = OWDistanceFileDropHandler()
-        self.assertTrue(handler.canDropFile("test.dst"))
-        self.assertTrue(handler.canDropFile("test.xlsx"))
+        self.assertTrue(handler.canDropFile(fn("xlsx_files/distances_with_nans.xlsx")))
+        self.assertFalse(handler.canDropFile(fn("xlsx_files/distances_nonsquare.xlsx")))
+        self.assertFalse(handler.canDropFile(fn("datasets/lenses.tab")))
         self.assertFalse(handler.canDropFile("test.bin"))
 
     def test_parametersFromFile(self):