Initially reported as magnitude 7.0, it was reduced to 6.8 by the US Geological Survey.
Electricity in the main town, also called Zante, was down while the fire service reported damage to the road network caused by landslides.
The natural disaster could be felt along western Greece, but was felt the strongest in the capital of Athens which is northeast of Zakynthos.
The power cut and slight damage to the port of Zakynthos, near the epicentre, would not affect port operations, officials said.
But Zakynthos Mayor Pavlos Kolokotsas said: "We are not facing any particular problems".
Describing the tremors, one person living in Greece told EMSC they felt: 'Extremely violent shaking. Since then all buildings have been fortified to protect against further tremors.
The Kingdom of Saudi Arabia risks isolation over Khashoggi killing | Money Talks
British Prime Minister Theresa May said its Saudi arms sales were "under review", a stance similar to that expressed by Australia. They also photographed Saudi diplomatic vehicles scouting wooded areas in the days before Khashoggi disappeared.
Both the US Geological survey and the European-Mediterranean Seismological Centre both assessed the natural disaster to be of a manitude of 6.8.
The main harbour for the island in the Ionian Sea was damaged but still functional, civil protection agency press spokesman Spyros Georgiou said.
The quake was fairly shallow, according to the USGS, just 14km (8.7 miles) below the seabed.
It said there was a low likelihood of casualties.
However, in July 2017 a magnitude 6.7 natural disaster killed two people on the island of Kos in the Aegean sea, causing significant damage.
In particular the natural disaster was felt on Zakynthos, where a series of after shocks were strong, with the highest figure being 5.6.