diff --git a/Lib/importlib/_bootstrap.py b/Lib/importlib/_bootstrap.py
--- a/Lib/importlib/_bootstrap.py
+++ b/Lib/importlib/_bootstrap.py
@@ -922,9 +922,12 @@
         raise TypeError('module name must be str, not {}'.format(type(name)))
     if level < 0:
         raise ValueError('level must be >= 0')
-    if package:
+    if level > 0:
         if not isinstance(package, str):
             raise TypeError('__package__ not set to a string')
+        elif not package:
+            raise ImportError('attempted relative import with no known parent '
+                              'package')
         elif package not in sys.modules:
             msg = ('Parent module {!r} not loaded, cannot perform relative '
                    'import')
diff --git a/Lib/test/test_importlib/import_/test_relative_imports.py b/Lib/test/test_importlib/import_/test_relative_imports.py
--- a/Lib/test/test_importlib/import_/test_relative_imports.py
+++ b/Lib/test/test_importlib/import_/test_relative_imports.py
@@ -218,6 +218,11 @@
             self.__import__('a', {'__package__': '', '__spec__': None},
                             level=1)
 
+    def test_relative_import_no_package_exists_absolute(self):
+        with self.assertRaises(ImportError):
+            self.__import__('sys', {'__package__': '', '__spec__': None},
+                            level=1)
+
 
 (Frozen_RelativeImports,
  Source_RelativeImports