The USGS said the epicentre of the quake was in the Aegean sea 11 kilometres south of Plomari, a village on the southern coast of Lesbos.
The mayor of Plomari, Manolis Armenakas, told ERT state television: "We have damage to several buildings, old and new. We are now evaluating the damage."
Reports said the quake was also strongly felt in the Karaburun district of Turkey's Izmir Province, as well as in Athens, Greece. There were no immediate reports of damage or casualties in Turkey.
Turkey and Greece sit on significant fault lines and have regularly been hit by earthquakes in recent years.
This year alone, Turkey's western Aegean coast was hit by several earthquakes of up to 5.5 magnitude, which brought back memories of past deadly earthquakes.
On August 17, 1999, a huge earthquake measuring more than 7.0 magnitude near the city of Izmit devastated vast zones in the country's densely populated northwestern zone, notably around Istanbul, killing over 17,000 people.