The raft, which was transporting Afghan and Iranian migrants to the Greek island of Lesbos, foundered just 500 meters from the Turkish coast of Ayvacık in the province of Çanakkale.
Turkish coastguards managed to save nine of the refugees on board while two were still missing.
The fresh tragedy came as the European Union and Turkey are trying to firm up a proposed deal to end the worst migration crisis to hit the continent since World War II.
On March 7, Turkey proposed a deal that would see the EU resettle one Syrian refugee from camps in Turkey in exchange for every Syrian that Turkey takes from Greece, in a bid to reduce the incentive for people to board boats for Europe.
In return, Turkey wants financial aid, visa-free access to Europe's passport-free Schengen zone and a speeding up of Ankara's efforts to join the EU.
EU leaders hope to finalize the deal at a summit on March 17-18.