The middle-aged victim had been trapped for around seven hours in the ruins of her home in the Lesbos village of Vrisa, the area that bore the brunt of the strong quake and where several homes collapsed.
"Our fellow citizen who was trapped in the house that collapsed in Vrisa was pulled out dead," Lesbos mayor Spyros Galinos said in a tweet.
The earthquake also struck the Aegean coast of western Turkey after 1200 GMT.
Video footage shot by a Vrisa resident on a cellphone showed masonry from several single and two-level homes clogging the streets.
"It's a difficult situation, we are facing a disaster," Christiana Kalogirou, governor of the north Aegean region, told Greek state TV station ERT, adding: "Some 10 people are injured."
"The army is bringing in tents so people can spend the night," she said, adding that the south of Lesbos had taken the brunt of the quake.
The tremor, felt as far as Athens and Izmir in Turkey, damaged at least three churches and shops in south Lesbos, local owners said, while rock slides blocked some roads.
"The street is full of plaster. I hope this peters out because people are very distressed," said Yiorgos Patarelis, a shop owner in the nearby port of Plomari.
Lesbos Deputy Mayor Manolis Armenakas told ERT: "We have damage to several buildings, old and new."
Infrastructure Minister Christos Spirtzis said two people had been hospitalised.
In Vrisa, a traditional village inhabited mainly by elderly people, "dozens of homes have collapsed and village roads are blocked," regional fire service supervisor Marios Apostolides told ERT.
Engineers were sent in from Athens to assess the damage and vet damaged homes.
The US Geological Survey said the epicentre of the quake was in the Aegean sea 11 kilometres (6.8 miles) south of Plomari, and there were several aftershocks.
The Athens Geodynamic Institute said the quake had a depth of just 10 kilometres.
"If this quake had happened on land the consequences would have been far greater," said seismologist Costas Papazachos.
Lesser damage was reported on Chios and there were no reports of damage or casualties at the refugee camps in the east and north of Lesbos.
AFP reporters in Izmir, Turkey's third-largest city, said the earthquake was felt in the centre and caused alarm among residents but there were no immediate reports od casualties from there.
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 has been hit by several earthquakes of up to 5.5 magnitude, which brought back memories of past deadly earthquakes.
On August 17, 1999, an 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.
A month later, a 5.9-magnitude quake killed 143 people in Athens and the region northwest of the capital.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)
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