The boat, carrying some 50 migrants, struck trouble after leaving the western Turkish resort of Foca in the Izmir region for the Greek island of Lesbos.
Twenty-eight people were saved while up to dozen more are still feared missing, NTV television said.
Turkey, which is home to some 2.2 million refugees from Syria's civil war, has become a hub for migrants seeking to reach Europe, many of whom pay people smugglers thousands of dollars for the risky crossing.
Brussels vowed to provide three billion euros as well as political concessions to Ankara in return for its cooperation in tackling Europe's worst migrant crisis since World War II.
But onset of winter and rougher sea conditions do not appear to have deterred the migrants, with boats still arriving on the Greek islands daily.
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