The main harbour for the island in the Ionian Sea was damaged but still functional, civil protection agency press spokesman Spyros Georgiou said.
Power was lost in the island capital and main town, also called Zakynthos, but no major damage was reported there.
“We’re checking out the villages on the island, where there are several older buildings,” Mr Georgiou said. “The lack of electricity is a problem, but technicians are trying to restore power.”
The fire service said 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. A couple of people were treated for minor injuries.
Mr Georgiou said a precautionary tsunami warning was issued, although none had materialised two hours after the earthquake.
The US Geological Survey said the undersea quake was magnitude 6.8 and its epicentre was 20 miles south-west of Mouzaki in the southern part of the island.
It had a depth of nine miles and struck just before 2am local time (11pm GMT Thursday).
Greece’s main earthquake monitoring centre, Athens’ Geodynamic Institute, measured the magnitude at 6.4, and said it had a depth of three miles. Measurements of quake strength can vary due to the equipment each institution uses and other factors.
The earthquake rattled the whole of western Greece and was strongly felt in the capital, 174 miles to the north-east of Zakynthos.
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.
Zakynthos has had severe earthquakes in the past, and as a result has a very strict building safety code.