The Turkish coastguard recovered the bodies from the wooden boat that had set off from the Turkish holiday resort town of Bodrum for the Greek island of Leros, the Dogan news agency reported.
The refugees drowned when they failed to get out of the boat’s cabin, the news agency said.
Another 20 migrants, who were on the boat’s deck, survived and swam back to the Turkish coast, it added. All were wearing life jackets.
The survivors were taken to a morgue in Bodrum to identify their drowned relatives.
There has been a sharp spike in the numbers of migrants and refugees setting out from Turkey in flimsy boats for the European Union in search of better lives.
Most are fleeing conflicts and misery in Syria, Afghanistan, Pakistan and Africa.
The picture of three-year-old Syrian refugee Aylan Kurdi, whose body was found washed up on a Turkish beach after a failed attempt to reach Greece, horrified the world, pressuring European leaders to step up their response to the refugee crisis.