The ship is believed to have sunk about 260 km from the Turkish coast, south of the tourist resort of Kas in the southern Turkish province of Antalya.
The nationality of migrants is still unknown.
Since 2014, more than 22,000 people have died trying to reach Europe across the Mediterranean.
The route across the eastern Mediterranean - from Turkey to Greece - is one of the most common routes for migrants, who often risk their lives in substandard and overcrowded boats.
So far, 37 people have been rescued, the country's defense ministry said.