Around a dozen others, mostly Afghans, are still missing after the rickety vessel, carrying 60 people, went down at dawn as it made the perilous crossing from Turkey, according to the Greek coastguard.
Many of those crossing the Aegean Sea from Turkey to Greece do not know how to swim and are often equipped with poor-quality life vests, the coastguard said.
A patrol boat and a helicopter operated by European border agency Frontex found the lifeless bodies of the woman and two children.
Despite worsening weather that has made the journey from Turkey to Greece even more dangerous, a record 48,000 refugees and migrants arrived this week in Greece, most of them in Lesbos, the International Organization for Migration said Friday.
Of more than 600,000 people who have reached Europe's shores this year in the continent's worst migration crisis since World War II, some 3,000 have died.