The bodies of the dead, also including two women, were discovered along the shore in the western province of Aydin, the private Dogan news agency reported.
Seven others were picked up alive, the agency said, adding that all of those on board were Syrian refugees.
The boat capsized after strong waves and winds, Dogan reported, as it was probably attempting to reach the Greek island of Samos.
Two Turkish suspected people-smugglers who had been on the boat were also detained, the agency added.
But Ankara has raised alarms in Brussels by threatening in recent weeks to scrap the agreement, which came into force after an estimated 1.26 million migrants reached Europe in 2015.
Europe and Turkey are locked in a bitter dispute after Turkish ministers were blocked from campaigning on the continent for a "yes" vote in next month's referendum on boosting President Recep Tayyip Erdogan's powers.
According to the International Organization for Migration, there were around 363,000 migrant arrivals in Greece in 2016 after the Turkey-EU accord.
Ankara has also criticised the EU for failing to fulfil its promise to give visa-free travel in the Schengen zone nations to Turks as part of the agreement.
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