Greece's coastguard said 57 people had been rescued on Tuesday, while seven people - two girls, four women and a man - were pulled from the water unconscious and later confirmed dead.
A search and rescue operation in the area off the eastern Aegean island of Lesbos was called off after all those on board had been accounted for, the coastguard said.
There were no further passengers reported missing.
It was not immediately clear why the boat capsized, and the coastguard did not provide further details on the incident or the nationality of the refugees and migrants.
"This tragedy is a painful reminder that people continue to take perilous journeys to reach the Greek Aegean islands," said Philippe Leclerc, the UNHCR representative in Greece.
"Redoubled efforts are needed to ensure safe and legal ways to reach Europe, so people stop risking their lives in the hands of ruthless traffickers and smugglers."
Greece became one of the main gateways for refugees entering Europe in recent years, many of them fleeing conflict in countries like Syria and Afghanistan, in the continent's worst migration crisis since World War II.
The number of people heading to the Greek islands from the nearby Turkish coast has decreased significantly since the height of the refugee crisis in 2015, dropping from 875,000 in 2015 to under 40,000 a year in 2017 and 2018, according to Frontex, the European Union's border force.
However, hundreds of people continue to make the treacherous journey.
Although the distance from Turkey is short, smugglers often use unseaworthy boats and pack them way beyond capacity, leading to many sinking or capsizing.
Nearly 10,700 refugees and migrants have reached Greece so far this year by sea, and 39 people have lost their lives while attempting the journey, the UNHCR said.
The influx of migrants and refugees to Greece was drastically curtailed by a 2016 accord between Turkey and the EU.
Greece is hosting some 70,000 mostly Syrian refugees and migrants who have fled their countries since 2015 and crossed over from neighbouring Turkey.
More than 300 refugees and migrants have died this year in total while trying to cross the Mediterranean to Europe, according to the International Organisation for Migration.