diff --git a/pandas/io/common.py b/pandas/io/common.py
index 54f35e689aac8..d1305c9cabe0e 100644
--- a/pandas/io/common.py
+++ b/pandas/io/common.py
@@ -18,6 +18,7 @@
     Optional,
     Tuple,
     Type,
+    Union,
 )
 from urllib.parse import (
     urljoin,
@@ -452,7 +453,7 @@ def get_handle(
     except ImportError:
         need_text_wrapping = (BufferedIOBase, RawIOBase)
 
-    handles: List[IO] = list()
+    handles: List[Union[IO, _MMapWrapper]] = list()
     f = path_or_buf
 
     # Convert pathlib.Path/py.path.local or string
@@ -535,6 +536,8 @@ def get_handle(
         try:
             wrapped = _MMapWrapper(f)
             f.close()
+            handles.remove(f)
+            handles.append(wrapped)
             f = wrapped
         except Exception:
             # we catch any errors that may have occurred
diff --git a/pandas/tests/io/parser/test_common.py b/pandas/tests/io/parser/test_common.py
index 3d5f6ae3a4af9..1d8d5a29686a4 100644
--- a/pandas/tests/io/parser/test_common.py
+++ b/pandas/tests/io/parser/test_common.py
@@ -1836,6 +1836,7 @@ def test_raise_on_no_columns(all_parsers, nrows):
         parser.read_csv(StringIO(data))
 
 
+@td.check_file_leaks
 def test_memory_map(all_parsers, csv_dir_path):
     mmap_file = os.path.join(csv_dir_path, "test_mmap.csv")
     parser = all_parsers