diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index 78eba8df..5a32a625 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -4,7 +4,8 @@ Changelog
 *unreleased*
 ~~~~~~~~~~~~
 
-No unreleased changes.
+* Handle ``OSError`` on non-dynamic executables when attempting to resolve
+  the glibc version string.
 
 20.4 - 2020-05-19
 ~~~~~~~~~~~~~~~~~
diff --git a/packaging/tags.py b/packaging/tags.py
index 9064910b..e35bbdad 100644
--- a/packaging/tags.py
+++ b/packaging/tags.py
@@ -474,8 +474,20 @@ def _glibc_version_string_ctypes():
     # main program". This way we can let the linker do the work to figure out
     # which libc our process is actually using.
     #
-    # Note: typeshed is wrong here so we are ignoring this line.
-    process_namespace = ctypes.CDLL(None)  # type: ignore
+    # We must also handle the special case where the executable is not a
+    # dynamically linked executable. This can occur when using musl libc,
+    # for example. In this situation, dlopen() will error, leading to an
+    # OSError. Interestingly, at least in the case of musl, there is no
+    # errno set on the OSError. The single string argument used to construct
+    # OSError comes from libc itself and is therefore not portable to
+    # hard code here. In any case, failure to call dlopen() means we
+    # can proceed, so we bail on our attempt.
+    try:
+        # Note: typeshed is wrong here so we are ignoring this line.
+        process_namespace = ctypes.CDLL(None)  # type: ignore
+    except OSError:
+        return None
+
     try:
         gnu_get_libc_version = process_namespace.gnu_get_libc_version
     except AttributeError:
diff --git a/tests/test_tags.py b/tests/test_tags.py
index 4840e196..0e445f2b 100644
--- a/tests/test_tags.py
+++ b/tests/test_tags.py
@@ -389,6 +389,13 @@ def test_glibc_version_string_ctypes_missing(self, monkeypatch):
         monkeypatch.setitem(sys.modules, "ctypes", None)
         assert tags._glibc_version_string_ctypes() is None
 
+    def test_glibc_version_string_ctypes_raise_oserror(self, monkeypatch):
+        def patched_cdll(name):
+            raise OSError("Dynamic loading not supported")
+
+        monkeypatch.setattr(ctypes, "CDLL", patched_cdll)
+        assert tags._glibc_version_string_ctypes() is None
+
     def test_get_config_var_does_not_log(self, monkeypatch):
         debug = pretend.call_recorder(lambda *a: None)
         monkeypatch.setattr(tags.logger, "debug", debug)