“The mother and the baby are also in good health,” the official said.
The migrants were found on the islet of Barbalias, about three kilometers (two miles) east of Lesbos and around 20 kilometers (12 miles) from the Turkish coast. Local officials said the baby was a boy.
Lesbos was the busiest entry point into the European Union during the 2015-16 crisis when hundreds of thousands of refugees and migrants fled war in Iraq, Syria and elsewhere.
But Greece has steadily toughened its migration policies, and many leaving Turkey now take the longer and more dangerous route to Turkey.
Over the weekend, the coast guard rescued 108 migrants from a leaking and rudderless sailboat near the holiday island of Mykonos.
Separately Wednesday, a man believed to be a migrant was found dead in the trunk of a car in an artificial lake near the Greek-Turkish border. Border police officers had pursued the vehicle after the driver refused to stop for a highway inspection. Five other passengers, all also believed to be migrants who had entered the country illegally, and the driver were detained, police said.
Costas Kantouris reported from Thessaloniki, Greece. Derek Gatopoulos in Athens, Greece contributed to this report.