It is possible to prevent new users from registering themselves on your MediaWiki site. For that, you need to edit your LocalSettings.php file.
Find the place on your LocalSettings.php where you have the $wgGroupPermissions declarations and add the following in a new line:
$wgGroupPermissions['*']['createaccount'] = false;
If you have no $wgGroupPermissions already defined in your file, just add the line anyway.
Make sure to check that such a line is not defined elsewhere in the file, whatever the settings in it.