The rescue operation of the migrants, 52 men, 11 women and 27 children, from the islet of Prasonisi, some 7.5 kilometres northwest of Antikythira was completed on Friday, officials said.
Seven bodies were recovered and a search operation was continuing.
Thursday's wreck was the second in the Aegean Sea this week. Overnight between Tuesday and Wednesday a boat thought to be carrying up to 50 people, also migrants, sank off the island of Folegandros, with dozens feared missing.
Antikythera and Folegandros are not on the typical route for migrants, and officials said the boats, which set off from Turkey, were likely to have been aiming for Italy.
The UNHCR estimates that more than 2,500 people died or went missing at sea while attempting to reach Europe this year.
Greece, on the front-line of Europe's refugee crisis when it began in 2015, is one of the main routes into the European Union for refugees and migrants fleeing war and poverty in the Middle East, Africa and Asia. Most cross on rubber boats to islands close to the Turkish coast.
The country has since hardened its stance and boosted land and sea patrols to deter people from reaching its shores.