The coastguard located and rescued 24 people from the vessel in the eastern Aegean Sea early today.
But they said five people were missing, four of them children, and a search and rescue effort is under way, the agency reported.
This new incident comes more than a week after international public opinion was appalled by the bleak image of a Syrian toddler, Aylan, lying face down on a Turkish beach.
The boy drowned along with his mother and brother when their boat capsized on a short run from Turkey to the Greek island of Kos and hopes of a new life in Europe.
Greece's minister in charge of shipping, Christos Zois, said yesterday that the situation in Lesbos, the Greek island struggling with a huge influx of migrants "is getting normalised".
He added that 22,500 migrants and refugees were taken to Athens this week.