Wow, that's a lot of deleted comments - I'll try to keep as relevant as possible. After a lot of research, I'm afraid that I'm empty handed. Certainly we can make assumptions (But I'm worried that might lead to a removal) since there are sections in the Qu'ran that are against the use of magic outside that divined by Allah and his prophets, but there has been records of magicians, though in the realm of western biased sources with more fascination of the European theatre. I did, however, find some sources from Michigan State University (Great History School) with several queries which include answers and interesting answers as well as references to books that I'm having trouble getting a hold of. To what I can find, there are cases of punishment towards those who practice "dark magic" as opposed to more divine "good magic". There aren't the same kinds of cases that you would find, since you didn't exactly have the same cultural context and societal factors that made the European and early Colonial witch hunts spring up.
From the perspective of someone who works on early Islamic and medieval Middle East, you don't see a lot of references necessarily to anything like witchcraft and you certainly don't see records of the kinds of witchcraft hysterias that spread throughout Western Europe and the Americas. The biggest no-nos in this direction would be alchemy because alchemists were often accused of trying to create life (bringing clay birds to life for example) which is essentially trying to play God.
If I were to make a few educated guesses why you don't see a lot of discussion of witchcraft, here's what I would say...
There were enough sectarian rivalries with real political implications (in that belonging to a sect meant you were also implicated in a group political aspiration) that you didn't have to bother with ridiculous accusations of witchcraft. You could just accuse someone of being a Shi'ite and then the government might get worried and have that person arrested or worse.
There were a lot of outlets for mystical tendencies within Islam. The formalization and rapid spread of Sufism by the end of the 10th century gave most Muslims access to experiential and mystical approaches to their faith in a rather mainstream form (that is not to say there weren't Sufi movements that were labeled ghulat or extremist in that they went too far with some of their ideas, most often in applying divinity to Muhammad, `Ali, or the founder of the order).
Magic in the form of amulets, astrology, numerology, mystical interpretation of letters (ilm al-huruf, similar to Hebrew gematria) appears to be extremely widespread and incorporated into more mainstream Sufi practices despite being officially looked down upon. The study of "magic" by modern historians is something that is only now picking up steam. Noah Gardiner is a historian at the forefront of this for the 13th century who has argued that the study of "magic" was often intertwined with the study of Sufi practices (see his article "Forbidden Knowledge?: Notes on the production, transmission, and reception of the major works of Ahmad al-Buni," Journal of Arabic and Islamic Studies, vol. 12 (2012), pp. 81-143 and watch for his recently completed dissertation).
I apologize for the scant references here, but it's difficult to supply references for a topic that hasn't been treated that much.
I think this begs the related question, "how true was the stereotype of Christian areas being paranoid about witches?"
In the time of Mohammad and in the century or so that followed, it appears from the Hadith (the collection of tales from his companions) that witchcraft was a concern - see below - but there is no evidence that there was witchcraft paranoia such as was seen in Europe. In contrast and as an example, the Islamic reaction to Zoroastrian religious practices in Persia is documented by scholars of the period.
In the Hadith narrated by Bukhari (Volume 7, Book 71, Verse 660), Aisa recollects Mohammed talking about and remedying a spell having been worked upon him. In the 661, 663, 664, other narrators also talk of a basic defense (eating dates) against witchcraft and magic. For context, I recommend reading on to verse 667 which addressed mange among camels at similar length. These hadith in a easy translation can be read at: http://www.usc.edu/org/cmje/religious-texts/hadith/bukhari/071-sbt.php
I respect that there are mixed views in the acceptance of the Hadiths and their authentication process as historical documents, but am asserting them as a possible historical source based in part on Humphreys, R. Stephen (1991). Islamic History: A framework for Inquiry (Revised ed.). Princeton University Press.
No, they didn't. While Islam does have similar beliefs as Christianity surrounding witches and witchcraft, they did not go on mass witch hunts or anything like that. It was regarded as an individual evil, single people being possessed by "the evil eye", not something that multiple people would engage in and that could spread.
Source: Historical Dictionary of Witchcraft
EDIT: screwed up the link