The collision occurred in the dark near the Aegean island of Kos, the coastguard said, adding that the migrant boat, carrying 34 people, had no lights on.
A man and a three-year-old child were reported missing while the injured and survivors were taken to a hospital on Kos.
Two of the injured were in a serious condition, including a pregnant woman, the coastguard said.
Riots at Greek migrant camp after killer blaze
Greece is facing increased arrivals of migrants and refugees from neighbouring Turkey, with hundreds landing daily.
The government has vowed to stiffen its response with stepped-up patrols to deter migrant boats.
"Waves of refugees and economic migrants are now besieging European countries," conservative Prime Minister Kyriakos Mitsotakis said last week.
Mitsotakis, who came to power in July, plans to also send 10,000 people back to Turkey and to speed up asylum procedures for refugee status applicants.
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