I looked at Raskas' blog and saw how he did it and applied the similar idea to MediaWiki 1.9.1 to make it work with Apache authentication mechanism. It takes only 2 steps:
1- Edit LocalSettings.php and append the following right before the php section ends with "?>"
# Apache::mod_auth integration
$wgAuth = new Auth_remoteuser();
# Disable anonymous edits
$wgGroupPermissions['*']['edit'] = false;
2- Download the following file: Auth_remoteuser.php.txt, rename it to "Auth_remoteuser.php" and put it in the following directory "extensions".