"The lack of electricity is a problem, but technicians are trying to restore power".
The biggest shock was felt as far afield as Naples in western Italy, and in Albania, Libya, and the capital Athens.
Hundreds of residents in Zakynthos spent the night in the streets in fear of more earthquakes, videos shot from inside stores and homes the moment the quake hit show the extent of the force of the tremor and tens of aftershocks were felt.
From first reports, immeasurable damage has occurred at the Tower of the Castro Monastery in Strofades.
The USGS said the undersea quake had a depth of 14 kilometers. A couple of people were treated for minor injuries.
Residents also left their homes in the city of Patras on the Greek west coast, reports said.
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The quake has caused damage to a harbour in Zakynthos, with images depicting the pavement warped and cracked close to moored boats.
It struck at 1:54 a.m. (2254 GMT on Thursday) and was followed by a series of moderate aftershocks.Greece straddles two tectonic plates and often gets earthquakes.
The Greek tourist island, popular with Brits, is understood to have been the epicentre.
Greece suffers from thousands of earthquakes per year, due to the area lying on one of the world's most quake prone regions.
A major 6.8 quake in Greece at 12.54 am local time is not expected to cause damage. In 1999, a magnitude 5.9 quake on the outskirts of Athens killed 143 people.
However, first pictures on Friday showed a large crack in the ground at the island's port.