Two migrants swam to shore not far from the coastal town of Dikili in Izmir province after their boat sank, the coastguard said in a statement, adding that a search was underway for those missing.
Dikili is on the opposite coast of the Greek island of Lesbos.
The group included 14 Afghan and one Iranian nationals. The missing migrants include three children.
Turkey hosts more than three million Syrian refugees and up to 300,000 Iraqis.
Separately, Turkish security forces rounded up 73 illegal migrants including Iraqis, Iranians, Afghans and Pakistanis in the northwestern Turkish province of Kırklareli, the official Anadolu Agency reported on Monday.
The migrants were trying to reach Europe, it added. The Kırklareli province is on the border with Bulgaria.
Turkey has been a main transition route for migrants trying to get to Europe, especially since the start of the Syrian conflict in 2011.
The number of migrants coming to Europe has declined since the influx hit a peak in 2015 when more than a million people landed in Greece from Turkey, mainly via boats.
Turkey and the European Union reached a deal in 2016 to stem the flow of migrants, with Ankara agreeing to take back migrants landing on Greek islands in exchange for incentives including financial aid.