diff --git a/src/PIL/Image.py b/src/PIL/Image.py
index 67e068b06fa..662afadf43c 100644
--- a/src/PIL/Image.py
+++ b/src/PIL/Image.py
@@ -621,6 +621,8 @@ def close(self) -> None:
         more information.
         """
         if getattr(self, "map", None):
+            if sys.platform == "win32" and hasattr(sys, "pypy_version_info"):
+                self.map.close()
             self.map: mmap.mmap | None = None
 
         # Instead of simply setting to None, we're setting up a
diff --git a/src/PIL/ImageFile.py b/src/PIL/ImageFile.py
index 1bf8a7e5f21..425dda60bef 100644
--- a/src/PIL/ImageFile.py
+++ b/src/PIL/ImageFile.py
@@ -34,7 +34,6 @@
 import logging
 import os
 import struct
-import sys
 from typing import IO, TYPE_CHECKING, Any, NamedTuple, cast
 
 from . import ExifTags, Image
@@ -278,8 +277,6 @@ def load(self) -> Image.core.PixelAccess | None:
 
         self.map: mmap.mmap | None = None
         use_mmap = self.filename and len(self.tile) == 1
-        # As of pypy 2.1.0, memory mapping was failing here.
-        use_mmap = use_mmap and not hasattr(sys, "pypy_version_info")
 
         readonly = 0