A coast guard said in a statement the vessels foundered off the island of Samos near the Turkish coast before dawn Monday. It said 36 people were rescued from the sea.
A cruise ship, coast guard vessels, fishing boats and two search and rescue helicopters are combing the area for more survivors. The nationalities of the migrants are unknown.
Greece is a major entry point for people from poor or war-torn parts of Asia and Africa seeking a better life in the European Union. Fatal accidents are frequent as migrants risk the dangerous sea crossing from Turkey.