The Norman Atlantic was travelling from the Greek port of Patras to the Italian city of Ancona.
Nearby ships have been called in to rescue the passengers and crew but strong winds are hampering the operation, Greek authorities say.
There are no immediate reports of casualties.
Italian media say the fire broke out on the ferry's car deck early on Sunday morning.
Around 35 passengers were transferred to a nearby Greek ferry by lifeboat, Merchant Marine Minister Miltiadis Varvitsiotis said.
"This is a complicated rescue mission ... The visibility is poor and the weather conditions are difficult, but we are confident because there are a good number of ships in the area" he said.Italian and Albanian teams are also taking part in the rescue operation.
Ferries are an important mode of transport between Greece's hundreds of islands as well as neighbouring countries.
