Could a virus be preventing me from installing an Anti-virus?
If your device is not Rooted, it would be impossible for an App to block installation of another app.  If it is rooted, this is possible (anything is possible), but still very unlikely.

Bottom line, it is very, very unlikely that malicious software is blocking installation from the Play Store.

Things to try:


Try to install it directly on the device (ie. don't push from Web).
Clear the cache and data for the Play Store App