diff --git a/astroid/nodes/_base_nodes.py b/astroid/nodes/_base_nodes.py
index 3ef97b580c..c79fec799b 100644
--- a/astroid/nodes/_base_nodes.py
+++ b/astroid/nodes/_base_nodes.py
@@ -130,8 +130,11 @@ def do_import_module(self, modname: str | None = None) -> nodes.Module:
         # If the module ImportNode is importing is a module with the same name
         # as the file that contains the ImportNode we don't want to use the cache
         # to make sure we use the import system to get the correct module.
-        # pylint: disable-next=no-member # pylint doesn't recognize type of mymodule
-        if mymodule.relative_to_absolute_name(modname, level) == mymodule.name:
+        if (
+            modname
+            # pylint: disable-next=no-member # pylint doesn't recognize type of mymodule
+            and mymodule.relative_to_absolute_name(modname, level) == mymodule.name
+        ):
             use_cache = False
         else:
             use_cache = True
diff --git a/tests/test_inference.py b/tests/test_inference.py
index 29bf56ac2c..868c83bc5f 100644
--- a/tests/test_inference.py
+++ b/tests/test_inference.py
@@ -22,6 +22,7 @@
     Uninferable,
     arguments,
     helpers,
+    manager,
     nodes,
     objects,
     test_utils,
@@ -991,6 +992,16 @@ def test_import_as(self) -> None:
         self.assertIsInstance(inferred[0], nodes.FunctionDef)
         self.assertEqual(inferred[0].name, "exists")
 
+    def test_do_import_module_performance(self) -> None:
+        import_node = extract_node("import importlib")
+        import_node.modname = ""
+        import_node.do_import_module()
+        # calling file_from_module_name() indicates we didn't hit the cache
+        with unittest.mock.patch.object(
+            manager.AstroidManager, "file_from_module_name", side_effect=AssertionError
+        ):
+            import_node.do_import_module()
+
     def _test_const_inferred(self, node: nodes.AssignName, value: float | str) -> None:
         inferred = list(node.infer())
         self.assertEqual(len(inferred), 1)