The Norman Atlantic was travelling from Patras in Greece to Ancona in Italy.
Choppy seas and strong winds are hampering the rescue. Early reports that it was tilting have been denied.
One person has died and another injured, Greek and Italian officials say. 131 people have been rescued.
Most of those on board were Greek. Others came from Italy, Turkey, Albania, Germany and many other countries, officials said.
The British ambassador to Greece said officials were investigating reports that two Britons were on board.
Italian media say the fire broke out on the ferry's car deck early on Sunday morning.
"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," Greece Merchant Marine Minister Miltiadis Varvitsiotis said.
Some of the passengers were said to have taken to life boats
Passengers on life boat
Those who have managed to leave the ferry face the double challenge of high winds and cold water
Italian and Albanian teams are also taking part in the rescue operation.
One of the passengers told Greek TV station Mega: "On the lower deck, where the lifeboats are, our shoes were starting to melt from the heat."
The wife of one of the cooks told journalists she had had a call from her husband saying: "I cannot breathe, we are all going to burn like rats - God save us."
Ferries are an important mode of transport between Greece's hundreds of islands as well as neighbouring countries.
