One woman and seven men have been rescued, while authorities have been searching for two people missing who were believed to have reached the island, a Greek coast guard official said.
Some 13 migrants were on board the boat, according to their accounts, the official added.
Greece is one of the European Union's main entry points for migrants and refugees fleeing poverty and conflict in the Middle East, Africa and Asia.
About 32,800 people have arrived in Greece so far this year, according to data from the United Nations refugee agency UNHCR, about 27,000 of them by sea.
(Reporting by Angeliki Koutantou; Editing by Kim Coghill)
