The two vessels sank four miles off the coast of the Greek island of Samos. A search for the missing, involving two helicopters, a navy warship and a cruise liner, is in progress. One survivor, a child, 3, was transferred to an Athens hospital.
Officials have not determined the identities or nationalities of the migrants.
Thousands of migrants from war-torn African countries have been arriving in European Union countries in search of asylum. They typically depart North Africa in overcrowded and often unseaworthy boats and attempt to traverse the Mediterranean Sea. The numbers have increased since 2011, when unrest in North African countries, and a civil war in Syria, began.