diff --git a/news/8139.bugfix b/news/8139.bugfix
new file mode 100644
index 00000000000..5cb857c71ee
--- /dev/null
+++ b/news/8139.bugfix
@@ -0,0 +1,2 @@
+Correctly set permissions on metadata files during wheel installation,
+to permit non-privileged users to read from system site-packages.
diff --git a/src/pip/_internal/operations/install/wheel.py b/src/pip/_internal/operations/install/wheel.py
index 0b3fbe2ffc2..e7315ee4b52 100644
--- a/src/pip/_internal/operations/install/wheel.py
+++ b/src/pip/_internal/operations/install/wheel.py
@@ -8,6 +8,7 @@
 
 import collections
 import compileall
+import contextlib
 import csv
 import logging
 import os.path
@@ -32,17 +33,18 @@
 from pip._internal.utils.misc import captured_stdout, ensure_dir, hash_file
 from pip._internal.utils.temp_dir import TempDirectory
 from pip._internal.utils.typing import MYPY_CHECK_RUNNING
-from pip._internal.utils.unpacking import unpack_file
+from pip._internal.utils.unpacking import current_umask, unpack_file
 from pip._internal.utils.wheel import parse_wheel
 
 if MYPY_CHECK_RUNNING:
     from email.message import Message
     from typing import (
         Dict, List, Optional, Sequence, Tuple, Any,
-        Iterable, Callable, Set,
+        Iterable, Iterator, Callable, Set,
     )
 
     from pip._internal.models.scheme import Scheme
+    from pip._internal.utils.filesystem import NamedTemporaryFileResult
 
     InstalledCSVRow = Tuple[str, ...]
 
@@ -565,19 +567,27 @@ def is_entrypoint_wrapper(name):
         if msg is not None:
             logger.warning(msg)
 
+    generated_file_mode = 0o666 - current_umask()
+
+    @contextlib.contextmanager
+    def _generate_file(path, **kwargs):
+        # type: (str, **Any) -> Iterator[NamedTemporaryFileResult]
+        with adjacent_tmp_file(path, **kwargs) as f:
+            yield f
+        os.chmod(f.name, generated_file_mode)
+        replace(f.name, path)
+
     # Record pip as the installer
     installer_path = os.path.join(dest_info_dir, 'INSTALLER')
-    with adjacent_tmp_file(installer_path) as installer_file:
+    with _generate_file(installer_path) as installer_file:
         installer_file.write(b'pip\n')
-    replace(installer_file.name, installer_path)
     generated.append(installer_path)
 
     # Record the PEP 610 direct URL reference
     if direct_url is not None:
         direct_url_path = os.path.join(dest_info_dir, DIRECT_URL_METADATA_NAME)
-        with adjacent_tmp_file(direct_url_path) as direct_url_file:
+        with _generate_file(direct_url_path) as direct_url_file:
             direct_url_file.write(direct_url.to_json().encode("utf-8"))
-        replace(direct_url_file.name, direct_url_path)
         generated.append(direct_url_path)
 
     # Record details of all files installed
@@ -589,10 +599,9 @@ def is_entrypoint_wrapper(name):
             changed=changed,
             generated=generated,
             lib_dir=lib_dir)
-    with adjacent_tmp_file(record_path, **csv_io_kwargs('w')) as record_file:
+    with _generate_file(record_path, **csv_io_kwargs('w')) as record_file:
         writer = csv.writer(record_file)
         writer.writerows(sorted_outrows(rows))  # sort to simplify testing
-    replace(record_file.name, record_path)
 
 
 def install_wheel(
diff --git a/tests/unit/test_wheel.py b/tests/unit/test_wheel.py
index fc719e8905e..2350927541d 100644
--- a/tests/unit/test_wheel.py
+++ b/tests/unit/test_wheel.py
@@ -239,13 +239,19 @@ def prep(self, data, tmpdir):
         self.dest_dist_info = os.path.join(
             self.scheme.purelib, 'sample-1.2.0.dist-info')
 
+    def assert_permission(self, path, mode):
+        target_mode = os.stat(path).st_mode & 0o777
+        assert (target_mode & mode) == mode, oct(target_mode)
+
     def assert_installed(self):
         # lib
         assert os.path.isdir(
             os.path.join(self.scheme.purelib, 'sample'))
         # dist-info
         metadata = os.path.join(self.dest_dist_info, 'METADATA')
-        assert os.path.isfile(metadata)
+        self.assert_permission(metadata, 0o644)
+        record = os.path.join(self.dest_dist_info, 'RECORD')
+        self.assert_permission(record, 0o644)
         # data files
         data_file = os.path.join(self.scheme.data, 'my_data', 'data_file')
         assert os.path.isfile(data_file)
@@ -286,7 +292,7 @@ def test_std_install_with_direct_url(self, data, tmpdir):
         direct_url_path = os.path.join(
             self.dest_dist_info, DIRECT_URL_METADATA_NAME
         )
-        assert os.path.isfile(direct_url_path)
+        self.assert_permission(direct_url_path, 0o644)
         with open(direct_url_path, 'rb') as f:
             expected_direct_url_json = direct_url.to_json()
             direct_url_json = f.read().decode("utf-8")