diff --git a/pandas/io/excel/_base.py b/pandas/io/excel/_base.py
index 44254f54cbc7a..d4570498e3fc6 100644
--- a/pandas/io/excel/_base.py
+++ b/pandas/io/excel/_base.py
@@ -892,6 +892,12 @@ def sheet_names(self):
 
     def close(self):
         """close io if necessary"""
+        if self.engine == "openpyxl":
+            # https://stackoverflow.com/questions/31416842/
+            #  openpyxl-does-not-close-excel-workbook-in-read-only-mode
+            wb = self.book
+            wb._archive.close()
+
         if hasattr(self.io, "close"):
             self.io.close()
 
@@ -900,3 +906,7 @@ def __enter__(self):
 
     def __exit__(self, exc_type, exc_value, traceback):
         self.close()
+
+    def __del__(self):
+        # Ensure we don't leak file descriptors
+        self.close()
diff --git a/pandas/tests/io/excel/test_readers.py b/pandas/tests/io/excel/test_readers.py
index e4b7d683b4c3b..480407664285f 100644
--- a/pandas/tests/io/excel/test_readers.py
+++ b/pandas/tests/io/excel/test_readers.py
@@ -543,6 +543,7 @@ def test_read_from_pathlib_path(self, read_ext):
         tm.assert_frame_equal(expected, actual)
 
     @td.skip_if_no("py.path")
+    @td.check_file_leaks
     def test_read_from_py_localpath(self, read_ext):
 
         # GH12655
@@ -881,6 +882,7 @@ def test_excel_passes_na_filter(self, read_ext, na_filter):
         tm.assert_frame_equal(parsed, expected)
 
     @pytest.mark.parametrize("arg", ["sheet", "sheetname", "parse_cols"])
+    @td.check_file_leaks
     def test_unexpected_kwargs_raises(self, read_ext, arg):
         # gh-17964
         kwarg = {arg: "Sheet1"}
diff --git a/pandas/tests/io/excel/test_writers.py b/pandas/tests/io/excel/test_writers.py
index b1be0a1a2fece..e0cb75b0a6c99 100644
--- a/pandas/tests/io/excel/test_writers.py
+++ b/pandas/tests/io/excel/test_writers.py
@@ -809,6 +809,7 @@ def test_to_excel_unicode_filename(self, ext, path):
             )
             tm.assert_frame_equal(result, expected)
 
+    # FIXME: dont leave commented-out
     # def test_to_excel_header_styling_xls(self, engine, ext):
 
     #     import StringIO
diff --git a/pandas/util/_test_decorators.py b/pandas/util/_test_decorators.py
index b9c165140aaad..7669e729995d0 100644
--- a/pandas/util/_test_decorators.py
+++ b/pandas/util/_test_decorators.py
@@ -24,6 +24,7 @@ def test_foo():
 For more information, refer to the ``pytest`` documentation on ``skipif``.
 """
 from distutils.version import LooseVersion
+from functools import wraps
 import locale
 from typing import Callable, Optional
 
@@ -230,3 +231,24 @@ def documented_fixture(fixture):
         return fixture
 
     return documented_fixture
+
+
+def check_file_leaks(func):
+    """
+    Decorate a test function tot check that we are not leaking file descriptors.
+    """
+    psutil = safe_import("psutil")
+    if not psutil:
+        return func
+
+    @wraps(func)
+    def new_func(*args, **kwargs):
+        proc = psutil.Process()
+        flist = proc.open_files()
+
+        func(*args, **kwargs)
+
+        flist2 = proc.open_files()
+        assert flist2 == flist
+
+    return new_func