The Greek coast guard said 36 people, 32 men, three women and a child, were pulled out of the sea alive, together with the bodies of two women. A man's body was recovered later in the day, the coast guard said.
It was not immediately clear what caused the overloaded craft to overturn before dawn, about four miles north of the island of Samos near the Turkish coast.
The capsized craft were being towed to Samos.
Coast guard vessels, fishing boats and two search and rescue helicopters were combing the area for more survivors. A cruise ship that participated for several hours in the operation was later cleared to continue its journey.
More From This Section
The nationalities of the migrants were unknown. Despite the deep financial crisis that brought Greece to the brink of bankruptcy four years ago, the country remains a major entry point for people from poor or war-torn parts of Asia and Africa seeking a better life in the European Union.
Another 21 people have drowned since the beginning of the year. Over the weekend Greek coastguards rescued about 250 immigrants from the sea.