Error updating to wordpress 3.7.1

When using the automatic update it get’s stuck at:

Downloading update from http://wordpress.org/wordpress-3.7.1-no-content.zip…
Unpacking the update…

My hosting service tells me that httpdocs and wp-admin are both set to 777 to try to get the update in.
They receive the following error:

PHP Fatal error: Call to undefined function mbstring_binary_safe_encoding() in /var/www/vhosts/EXAMPLE.com/httpdocs/wp-admin/includes/class-wp-filesystem-direct.php on line 62, referer: http://EXAMPLE.com/wp-admin/update-core.php

I can still work on my website, but certain elements have gone missing. Any help would be greatly appreciated.