I've been facing the exact same injected script on several of my websites for the last few weeks. Today I realize these websites don't share the same hosting servers, yet the attacks (1) started at the same time (2) are identical.Does this prove that my FTP passwords have been stolen (they're all stored in Filezilla XML file on my hard drive) ? What else could be the security hole?
Script injection on different hosting servers = FTP hacking?
hacking
It is likely to be either the FTP passwords or some common software that is powering the sites.   For example it is very common for an old version of WordPress to be vulnerable to this type of an attack.You should:Change your FTP passwordsUpdate all the software powering your sites.Google just released a set of resources for Webmasters that have been hacked.  You may find more information there that is relevant to your situation.