Fifteen others were rescued when the six-metre boat sank in the early hours near the coast of the Aegean island.
The death toll from drowning among thousands of refugees making the short but dangerous crossing from Turkey to Greece's eastern islands has risen in recent weeks as autumn weather has set in, bringing high winds and falling temperatures.
"We recovered 11 drowned bodies, 10 of which were trapped inside the vessel's cabin," a coast guard official said, adding that the dead included four babies, two children and four women.
A search and rescue operation was continuing to find two more migrants missing from the boat.
Greece has been a transit point for more than 570,000 refugees and migrants fleeing conflict in the Middle East and beyond this year, putting European nations at odds over how to deal with the continent's biggest humanitarian crisis in decades.