I think it would be possible if the warheads of the A-A system were nuclear.
I see. So regular missiles won't do. I was able to find something that Russia calls the "Satan" missile which are specifically for "small space objects." Here is the link:I'm no expert but the way I see it.
Most anti-air missiles have a warhead between 10 and 100kg and they are designed to destoy aircraft or incoming missiles. Both obviously are not exactly the toughest of targets. Meteorites that will not be burned up in the atmosphere are going to be pretty large chunks of rock. So without having any deeper knowledge of the subject I would say that a regular anti-air missile won't do much, especially since the explosion would be on the surface (or in a lot of cases in the proximity of the surface) of the target.