diff --git a/changelogs/fragments/78648-urllib3-import-exceptions.yml b/changelogs/fragments/78648-urllib3-import-exceptions.yml
new file mode 100644
index 00000000000..35cb58dbe25
--- /dev/null
+++ b/changelogs/fragments/78648-urllib3-import-exceptions.yml
@@ -0,0 +1,5 @@
+bugfixes:
+- urls - Guard imports of ``urllib3`` by catching ``Exception`` instead of
+  ``ImportError`` to prevent exceptions in the import process of optional
+  dependencies from preventing use of ``urls.py``
+  (https://github.com/ansible/ansible/issues/78648)
diff --git a/lib/ansible/module_utils/urls.py b/lib/ansible/module_utils/urls.py
index 87c9e9061d7..4bf5f5d1bdb 100644
--- a/lib/ansible/module_utils/urls.py
+++ b/lib/ansible/module_utils/urls.py
@@ -126,19 +126,19 @@ try:
     HAS_URLLIB3_SSL_WRAP_SOCKET = False
     try:
         from urllib3.contrib.pyopenssl import PyOpenSSLContext
-    except ImportError:
+    except Exception:
         from requests.packages.urllib3.contrib.pyopenssl import PyOpenSSLContext
     HAS_URLLIB3_PYOPENSSLCONTEXT = True
-except ImportError:
+except Exception:
     # urllib3<1.15,>=1.6
     HAS_URLLIB3_PYOPENSSLCONTEXT = False
     try:
         try:
             from urllib3.contrib.pyopenssl import ssl_wrap_socket
-        except ImportError:
+        except Exception:
             from requests.packages.urllib3.contrib.pyopenssl import ssl_wrap_socket
         HAS_URLLIB3_SSL_WRAP_SOCKET = True
-    except ImportError:
+    except Exception:
         pass
 
 # Select a protocol that includes all secure tls protocols