I just read about this on Ars Technica and I too am wondering if Avast! Mobile Security & Antivirus will protect my phone from this.

Ars Technica - 2013-06-07 - Behold, the world’s most sophisticated Android trojan - Obad.a exploits undocumented Android bugs and offers advanced features.
http://arstechnica.com/security/2013/06/behold-the-worlds-most-sophisticated-android-trojan/