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http://wiki.openwrt.org/doc/howto/lamp

opkg update
opkg install mysql-server

sed -i 's,^datadir.*,datadir         = "/srv/mysql",g' /etc/my.cnf
sed -i 's,^tmpdir.*,tmpdir          = "/tmp",g' /etc/my.cnf

mkdir -p /srv/mysql
mysql_install_db --force
/etc/init.d/mysqld start
/etc/init.d/mysqld enable
mysqladmin -u root password 'password'

Test mysql-server:

root@Arduino:~# mysql -uroot -p
Enter password:
mysql> show databases;
+--------------------+
| Database           |
+--------------------+
| information_schema |
| mysql              |
| test               |
+--------------------+
3 rows in set (0.00 sec)