The boat occupants into the water as it lay immobilised in shallows east of the island, the coastguard said.
Fifteen other people were rescued, including two that required hospitalisation, it said.
An 18-year-old was arrested as a suspected trafficker.
Greece has been overwhelmed this year by a migration crisis unseen in Europe since World War II.
The United Nations on Friday said over 800,000 people have crossed the Mediterranean to Europe this year, with over 3,400 dying in the process.
Greek Prime Minister Alexis Tsipras will travel to Turkey next week to press the country's leaders to take a stronger stance against refugee traffickers.