More than 60 have been rescued from the sea near the Turkish resort of Ayvacik.
Local officials say they expect the death toll to rise when the capsized boat is searched.
Thousands of refugees and migrants continue to make the dangerous sea journey from Turkey to Greece to seek asylum in northern Europe.
The International Organization for Migration (IOM) said on Friday that 244 migrants had drowned in the Mediterranean so far this year, out of 55,568 arrivals.
“The daily average (of arrivals) is nearly equivalent to the total numbers for the month of January as recently as two years ago,” the IOM said.
The latest tragedy comes just days after 26 migrants drowned when their boat sank off the coast of the Greek island of Samos.
Last year more than one million migrants, many fleeing war, poverty and oppression, arrived in Europe, causing a political crisis among EU states.
The Turkish coastguard said that in Saturday’s incident the migrants had been trying to reach the Greek island of Lesbos when their boat capsized.
Lesbos is one of the most popular European arrival points for asylum seekers.
The deputy governor of Turkey’s Canakkale province, Saim Eskioglu, said the 17m (56ft) boat “hit rocks soon after it left the coast”.
“We believe there are more dead bodies inside the boat,” he told CNN-Turk TV.
Many of those rescued are being treated in hospital for hypothermia.
A Turkish man suspected of being the people smuggler who organised the trip has been arrested, according to Turkey’s Dogan news agency.
Those on board were from Afghanistan, Syria and Myanmar, Turkey’s Anadolu news agency said.
Last week, a draft European Commission report said Greece had “seriously neglected” its obligations to control the external frontier of Europe’s passport-free Schengen zone.
The Greek government accused the commission of playing “blame games”.
Late last year, the Turkish government signed a deal with the EU to receive about €3bn (£2.2bn; $3.3bn) in return for stemming the flow of asylum seekers.
However, the proposals have reportedly stalled amid objections from Italy.
Turkey is home to nearly three million refugees, most of them from Syria.
Many of them pay smugglers thousands of dollars to make the crossing to Greece. They then head north, with most trying to reach Germany, Austria and Scandinavia.