A video uploaded on Greek news website Proto Thema showed the 183-metre ferry engulfed in flames and huge plumes of smoke. "May Day" was blasting from speakers.
The coastguard said 239 passengers and 51 crew members were on board the Italian-flagged Euroferry Olympia and most of them had boarded rescue vessels transferring them to the port of the island of Corfu.
There were no immediate reports of deaths or severe injuries. One person with breathing problems had been taken to the hospital, according to the Athens News Agency.
The ferry had sailed from Igoumenitsa, the largest port in western Greece, and was headed to the Italian port of Brindisi, about nine hours away.
The fire, the cause of which was not immediately known, broke out near the island of Corfu in the Ionian Sea.
"We were woken up around 4.20am. Within an hour we had left the ship... We were saved by the crew, which acted fast," one of the passengers told Skai TV via telephone.
The ferry is part of the fleet of group Grimaldi Lines and has a capacity of up to 560 passengers, according to the company's website.
Grimaldi Lines spokesman Paul Kyprianou told Reuters that the cause of the fire was still under investigation but there were indications it started from the ship's hold.
"Damage is severe because despite the efforts the crew was unable to extinguish the fire," he said.
At least three coastguard vessels and one Italian financial police vessel were involved in the rescue operation.
Ship tracking data provided by Refinitiv Eikon showed the Euroferry Olympia performing a U-turn northwest of the North Corfu channel.
In 2014, 10 people were killed when a car ferry carrying 466 passengers and crew caught fire while sailing from Greece to Italy.
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