This is how I’ve enabled secure SSL login through https on a mediaWiki 1.13.3 installation. This description might work on other versions of mediaWiki, but that has not been tested.
mediWiki doesn’t support SSL login out of the box so a little hack has to be performed.

First you need to tell the webserver, in my case my Apache server that mediaWiki login requests should be redirected to the SSL page
Add the following code lines to your Apache config files or the mediaWiki .htaccess file

Rewrite login url to use httpsRewriteEngine On

RewriteCond %{REQUEST_URI} ^/index.php$
RewriteCond %{QUERY_STRING} ^title=Special:UserLogin
RewriteCond %{REQUEST_METHOD} ^GET$
RewriteRule ^(.*)$ https://%{SERVER_NAME}/$1 [R]

Rewrite non login url to use normal http

RewriteEngine On
RewriteCond %{QUERY_STRING} ^(?!title=Special:Userlogin)
RewriteRule ^(.*)$ http://%{SERVER_NAME}$1 [R]

Source: http://wiki.epfl.ch/cfavi/mediawiki

In addition to the above configuration you have to create a PHP script to fix some cookies problems since the cookie was made on an https address but normal surfing is done on http mode.

Create a file named ssl_login.php and insert the following code into it

# Secure the login page.

# Secure cookies hurt us because they are set on the https page
# but inaccessible from the http page, so we lose our previous session.
$wgCookieSecure = false;

# Don't process JavaScript and CSS files.
# Otherwise, a secure page will be tagged as "partially secure" because these
# files are being hit via http.
if (checkQS('gen', 'js')) {return;}
if (checkQS('gen', 'css') || checkQS('ctype', 'text/css')) {return;}

# Get page title from query string.
$pageTitle = array_key_exists('title', $_GET)
     ? $_GET['title']
     : "";

# Get server variables
$domain = $_SERVER['HTTP_HOST'];
$uri = $_SERVER['REQUEST_URI'];

# Are we on the sign-in page or not?
# Logic works for everything except Special pages which apparently don't
# even run LocalSettings.php.
$onSignInPage = false;
$signInPageName = 'special:userlogin';  // lowercase on purpose
if ( strtolower($pageTitle) == $signInPageName ) {
  $onSignInPage = true;
} elseif ( strstr(strtolower($uri), "/$signInPageName") ) {
  $onSignInPage = true;
} else {
  $onSignInPage = false;
}

# Secure only the Special:Userlogin page.
# Un-secure all other pages.
if ( !checkServerVariable('HTTPS', 'on') && $onSignInPage ) {
  header('Location: https://' . $domain . $uri);
} elseif ( checkServerVariable('HTTPS', 'on') && ! $onSignInPage ) {
  header('Location: http://' . $domain . $uri);
} else {
  // nothing
}

function checkQS($key, $value) {
  return checkArrayValue($_GET, $key, $value);
}

function checkServerVariable($var, $value) {
  return checkArrayValue($_SERVER, $var, $value);
}

function checkArrayValue($arr, $key, $value) {
  return array_key_exists($key, $arr) && $arr[$key] == $value;
}

Include this file in your LocalSettings.php file like this

# Fix to use SSL login
include '/full/path/to/htdocs/ssl_login.php';

Source: http://www.mediawiki.org/wiki/Manual:Configuration_tips_and_tricks#HTTPS_on_Login_only

Remember to restart your apache webserver to see the changes.