It would coincide with the European Middle Ages, but I am wondering whether or not the Mongol Empire (more specifically their invasion of the Kievan Rus') is considered to be during the Middle Ages.
The journal I am subscribed to is called Old Russia. The Questions of Middle Ages and the Mongol invasion is definitely among its topics. More than that, it calls Tatar-Turkic states of the 15th-18th centuries "medieval states" in the latest issue, so at least according to Russian historians the Middle Ages in Asia ended much later than you would expect.
edit: used the correct English name of the journal
The Kievan Rus were more interested in Europe than the rest of modern Russia. In general it depends on the region or culture of the conquest since the Mongolian Empire soread from China to Europe.