error: PHP is missing MySQL extension

I’ve created the wp-config.php file with DB_HOST, DB_NAME etc, and uploaded everything, but when I “open /wp-admin/install.php in your browser” (which I take to mean, go to https://www.mydomainname.com/wp-admin/install.php), I get:

“Your PHP installation appears to be missing the MySQL extension which is required by WordPress”.

Our hosting at GoDaddy.com runs PHP 5.x and MySQL 5.0 (with mysqli extension), and has been working fine as such.
What ‘extension’ does WordPress require? Can’t find any reference. Or is something else wrong? Any suggestions?
mike