On December 10, Canonical published details about MySQL vulnerabilities for its Ubuntu 12.10, Ubuntu 12.04 LTS, Ubuntu 11.10, and Ubuntu 10.04 LTS operating systems.
According to Canonical, MySQL could have been made to run programs if it received specially crafted network traffic from an authenticated user.
It was discovered that MySQL had incorrectly handled certain long arguments. A remote authenticated attacker could have used this issue to possibly execute arbitrary code.
For a more detailed description of the security problems in question, you can visit Canonical's security notification.
Users can simply fix the security flaws by upgrading the operating systems to the latest mysql-server package, specific to each distribution.
A normal system update, executed with the Update Manager, will implement all the necessary changes. A complete system restart is not necessary.