The wooden boat was believed to have been carrying around 21 people when it sank for reasons that were not immediately clear off the coast of the eastern Aegean island of Agathonisi, the coast guard said.
The drownings - the first such mass casualty in several months - came nearly exactly two years after Turkey and the European Union signed a deal to curb the flow of migrants trying to reach Europe via the Aegean Sea. Greek coast guard vessels assisted by two helicopters were searching for more survivors.
A Syrian woman carries a girl at the refugee camp of Ritsona about 86 kilometers north of Athens.
"We can not and must not tolerate people, children, losing their lives in the Aegean", Greece's Migration Minister Dimitris Vitsas said.
The number of new arrivals has decreased dramatically in recent months to a few dozen per day, according to Greek Coast Guard official figures.More news: Top Pakistan Security Official to Visit Afghanistan for Crucial Talks
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Another two migrants died near the land border with Turkey when the truck they were travelling in overturned trying to avoid a police check, authorities said.
European border agency Frontex said last month that in 2017, the European Union saw the lowest number of detected illegal border crossings since the migrant crisis began four years ago.
Hundreds of refugees and migrants perished in the Aegean Sea waters since 2015 when hundreds of thousands of people started risking their lives to cross into Greece from Turkey.
Under that deal, anyone who arrives on Greek islands must be returned to Turkey unless they qualify for asylum.