About 80 people were on board when the boat carrying refugees and migrants overturned, Greek national news agency AMNA said.
A total of 63 passengers were rescued and transferred to safety on the island, Greek newspaper Ethnos (Nation) reported.
This was the third tragedy in Greek waters within four days.
Earlier, Greece‘s Hellenic Coast Guard announced that the death toll from a refugee and migrant boat sinking on Thursday off the Aegean Sea island of Antikythera has reached 11, with 90 passengers rescued.
On Wednesday, the Greek authorities announced that a similar boat sank near Folegandros island, killing three people, and leaving 13 others rescued and an unknown number of people missing.
Greece has been at the forefront of the refugee and migrant influx since 2015. Hundreds have perished in the Aegean Sea in the past six years.
So far this year, Greece has launched more than 1,450 search and rescue operations and saved more than 29,000 people, Greek maritime affairs and insular policy minister Ioannis Plakiotakis said in an e-mailed press release on Saturday.
Traffickers usually stack dozens of distressed people without life jackets on boats that do not meet the basic safety standards, the minister said.