Huge, huge, influence on Islamic theological schools. It would not be a stretch to say that for certain theological schools, Aristotle was the most important influence. In particular, the Islamic Philosophers (i.e. Ibn Sina and Ibn Rushd) as well as their countermovements such as the Mu'tazila and then the Asharites. A lot of the kalam cosmological argument is very clearly borrowed from Aristotle's Metaphysics and the whole Ashari tradition of definition, proposition, logic, and dispute is very much influenced by Aristotle.

I don't think there was a lot of (any?) Aristotelian influence in the first couple hundred years of Islam, but by around 1000, Aristotle's Metaphysics had been translated into Arabic and was hugely important throughout the Middle Ages. The Stanford Encyclopedia of Philosophy page on Arabic and Islamic Metaphysics is pretty good: http://plato.stanford.edu/entries/arabic-islamic-metaphysics/