diff --git a/Lib/importlib/resources/readers.py b/Lib/importlib/resources/readers.py
index c3cdf769cbecb0..8e2d8e8250bd7e 100644
--- a/Lib/importlib/resources/readers.py
+++ b/Lib/importlib/resources/readers.py
@@ -31,8 +31,10 @@ def files(self):
 
 class ZipReader(abc.TraversableResources):
     def __init__(self, loader, module):
-        _, _, name = module.rpartition('.')
-        self.prefix = loader.prefix.replace('\\', '/') + name + '/'
+        self.prefix = loader.prefix.replace('\\', '/')
+        if loader.is_package(module):
+            _, _, name = module.rpartition('.')
+            self.prefix += name + '/'
         self.archive = loader.archive
 
     def open_resource(self, resource):
diff --git a/Lib/zipimport.py b/Lib/zipimport.py
index a7333a4c4906de..7669abd6c472e6 100644
--- a/Lib/zipimport.py
+++ b/Lib/zipimport.py
@@ -254,17 +254,9 @@ def load_module(self, fullname):
 
 
     def get_resource_reader(self, fullname):
-        """Return the ResourceReader for a package in a zip file.
-
-        If 'fullname' is a package within the zip file, return the
-        'ResourceReader' object for the package.  Otherwise return None.
-        """
-        try:
-            if not self.is_package(fullname):
-                return None
-        except ZipImportError:
-            return None
+        """Return the ResourceReader for a module in a zip file."""
         from importlib.readers import ZipReader
+
         return ZipReader(self, fullname)