I had no problem in installing it on a galaxy nexus and android 4.0.1.
However, hopefully you aren't trying or able to install the beta version as it has been released normally in the android market. Use the Market app icon on your phone and search for avastmobilesecurity and that should find it, after that it is Download as normal and it installs. That is the way I did it and no issues.
My galaxy nexus 4.0.1 isn't rooted and the install was fine, just that there are elements that can't be used if the phone wasn't rooted before installation, e.g. the firewall.