The tremor was felt in Greece's capital, Athens, and as far away as Italy and Albania.
Initial reports suggest it hit the Ionian sea, just off the western coast of Greece at just before 11pm local time.
The Greek tourist island, popular with Brits, is understood to have been the epicentre.
One witness posted online: "Me and my partner are staying in Zante, it woke my partner up, and we've had 3 aftershocks much smaller, the larger quake has moved several items around the room."
Greece's fire service said no damage has been reported so far, but power has been cut off in the island capital of Zakynthos.
Rockfalls were reported in another part of the island, and part of a church wall collapsed on the mainland town of Pyrgos, in the southern Peloponnese area.
Another two less strong shocks hit Zante just before and shortly after the magnitude 6.8 one.
Greece lies in one of the world's most earthquake-prone regions, with thousands of quakes recorded every year.
But few cause injuries or significant damage. In 1999, a magnitude 5.9 quake on the outskirts of Athens killed 143 people.
Zante has had severe earthquakes in the past, and as a result has a very strict building safety code.
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