Thirty-one migrants were rescued after the boat went down off the coast of Bodrum district in Mugla province, the coastguard added, with search and rescue efforts continuing.
The nationality of the migrants was not immediately known.
The incident took place a few kilometres (miles) from the Greek island of Kos.
Home to three million Syrian refugees and up to 300,000 Iraqis who have fled conflict, Turkey is a transit country for migrants trying to reach Europe.
Numbers have dropped since hitting a peak in 2015 when over a million people arrived in Greece fromTurkey, mostly via boats, during the worst refugee crisis since the Second World War.
But a March 2016 deal between Ankara and the European Union helped staunch the flow.
Arrivals on the Greek islands were 875,000 in 2015, dropping to under 40,000 per year in 2017 and 2018, according to EU border force Frontex.
Between January and June this year, 555 migrants died attempting to cross the Mediterranean, according to the International Organization for Migration.
The figure was 924 last year with a peak of 2,911 deaths recorded in 2016.