The boat was detected by a patrolling coastguard vessel at about 2 am (2300 GMT) north of Lesbos, Reuters reported.
So far 23 migrants have been rescued and a search and rescue operation is still ongoing, a coastguard official said. It was not immediately clear how many people may have been on the boat.
Greece, in the southeast corner of the European Union, has long been a favored gateway to Europe for migrants and refugees from the Middle East, Africa and Asia. In 2015, nearly one million people landed on its islands.
Last year, about 54,000 migrants reached Greece, the second largest number in southern Europe behind Italy. The vast majority of them arrived by sea, according to data from the UNHCR.