When will Unity Web Player be officially released on Linux?

Unity Technologies still do not provide a Unity Web Player for Linux browsers. I also haven't heard any plans on doing so.

Workaround:

Previously Linux users tried to install Windows versions of internet browsers to run the Unity Web Player using Wine.

The Pipelight project has made a plugin for native Linux browsers. It still uses Wine, but at least you won't deal with Windows versions of internet browsers. See the community set up wiki page - http://wiki.unity3d.com/index.php/Running_Unity_Web_Player_on_Linux_using_Pipelight