In a sense this is a question that might have been better suited to the Short Answers segment of AH, and I hope the mods will not mind me answering it in that way.

Yes, parts of what is now Italy – specifically Sicily and possibly portions of the (much less-well-chronicled) island of Sardinia – were once part of Arab caliphates centred in the Middle East (though later they were ruled by successor states that were Muslim, but cannot really be considered to be "Middle Eastern" in any meaningful sense). The beginnings of the Arab conquest of Sicily date to 827, during the time of the Abbasid Caliphate, which had its capital in Baghdad, and an Emirate of Sicily endured until the Norman conquest which began in 1061. Sardinia was frequently raided by Islamic forces from 705 onwards, and it would seem likely there were some brief periods in which small parts of the coastal districts of the island were under Muslim control between that date and the 1050s – we simply have very little firm information about the period. The majority of these attacks would, however, have come from local Muslim rulers in Spain and North Africa rather than those based in the Levant.

The Muslim presence in mainland Italy was of much shorter duration, but there was also a short-lived Emirate of Bari, which was in existence for just over two decades from 847. Finally, there was a year-long Ottoman occupation of the port of Otranto in 1480-1.

Most detailed sources for all this are in Italian, but the Cambridge Medieval History and Alex Metcalfe's Muslims of Medieval Italy (2009) are both good places to start the search for additional information.