The coast guard said 237 passengers and 51 crew members were on board the Italian-flagged Euroferry Olympia and most of them had boarded rescue vessels.
There were no immediate reports of deaths or injuries, authorities said.
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.
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.
"We were woken up around 430am. The fire probably broke out in the garage," one of the passengers on board a rescue vessel told Mega TV via telephone.
At least three coast guard vessels and one Italian financial police vessel were involved in the rescue operation.
Ship tracking data provided by Refinitive Eikon showed the Euroferry Olympia performing a U-turn northwest of the North Corfu channel.
The evacuated passengers and crew were being taken to the port of Corfu, authorities said.
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.
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