diff --git a/news/6543.bugfix b/news/6543.bugfix
new file mode 100644
index 00000000000..6c06999c4f3
--- /dev/null
+++ b/news/6543.bugfix
@@ -0,0 +1 @@
+Work around failure to import ctypes when resolving glibc version string.
\ No newline at end of file
diff --git a/src/pip/_internal/utils/glibc.py b/src/pip/_internal/utils/glibc.py
index 5bea655ebcc..256552a42b2 100644
--- a/src/pip/_internal/utils/glibc.py
+++ b/src/pip/_internal/utils/glibc.py
@@ -1,11 +1,16 @@
 from __future__ import absolute_import
 
-import ctypes
 import re
 import warnings
 
 from pip._internal.utils.typing import MYPY_CHECK_RUNNING
 
+# Work around https://bugs.python.org/issue37060.
+try:
+    import ctypes
+except (ImportError, OSError):
+    ctypes = None
+
 if MYPY_CHECK_RUNNING:
     from typing import Optional, Tuple
 
@@ -14,6 +19,9 @@ def glibc_version_string():
     # type: () -> Optional[str]
     "Returns glibc version string, or None if not using glibc."
 
+    if not ctypes:
+        return None
+
     # ctypes.CDLL(None) internally calls dlopen(NULL), and as the dlopen
     # manpage says, "If filename is NULL, then the returned handle is for the
     # main program". This way we can let the linker do the work to figure out