Eighty people were believed to have been on the vessel which, according to the coastguard, was believed to have been headed for Italy from Turkey.
Air and sea assets were deployed to the area, the coastguard said early on Saturday.
Greece is one of the main routes into the European Union for refugees and migrants from Africa, the Middle East and beyond, though the flow has tapered off since 2015-2016 when more than a million people traversed the country to other EU states.
Earlier on Friday, Greek authorities said they had recovered 11 bodies from the scene of another shipwreck when a sailboat carrying refugees sank off an uninhabited islet in southern Greece on Thursday.
Ninety people were rescued in that operation.
Overnight between Tuesday and Wednesday, a boat thought to have been carrying up to 50 refugees sank off the island of Folegandros, with dozens feared missing.
The UN refugee agency UNHCR said the Folegandros accident was the worst in the Aegean Sea this year.
"This shipwreck is a painful reminder that people continue to embark on perilous voyages in search of safety," Adriano Silvestri, the UNHCR’s assistant representative in Greece, told the AFP news agency.
The UNHCR estimates that more than 2,500 people have died or gone missing at sea in their attempt to reach Europe from January through November this year.
Nearly one million people, mainly Syrian refugees, arrived in the European Union in 2015 after crossing to Greek islands close to Turkey.
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