The cruise ship Nordlys was sailing close to the port of Aalesund in western Norway when a fire started in the engine room.
Two crew members died and nine other crew were taken to hospital, with two being treating for serious burn and smoke injuries.
A police spokesperson said that although four people have been reported missing, this could not yet be confirmed.
Thick black smoke was seen rising from the liner as the 207 passengers and most of the 55 crew were evacuated at 9.20am (7.20am GMT). Some of the crew remained on board to try and subdue the fire.
The liner belongs to the Hurtigruten company which operates along Norway’s coast and through the fjords.
It was following a popular tourist route from Bergen to the northern regions above the Polar circle.
According to the company website, the MS Nordlys was built in 1994 and has a 691-passenger capacity.