Have you created a new DBMS user for Zabbix? Whatever the case, when you grant privileges, you have to specify that the user is allowed to connect from any host.
mysql> grant all privileges on zabbix.* to someusr@"%" identified by 'password';
If you use % it means any host.
Other than that your DBMS service should be bound to an IP address. Check your mysqld configuration file to do so.