Police said they received information that an additional four people were missing, but could not immediately confirm it. Nine people were taken to the hospital, two with serious burns and smoke injuries.
The MS Nordlys, with 262 people on board, was evacuated after it caught fire at 9:20 a.m. (0720 GMT) before arriving in Alesund, 230 miles (375 kilometers) northwest of Oslo. More than 100 passengers were evacuated into lifeboats before the ship reached port.
The remaining passengers and some crew left the vessel as smoke was still billowing from the burning ship. Hurtigruten ASA, the Norwegian operator of the ship, said eight of its crew were among those sent to hospital.
Police said they sealed off parts of Alesund because of the heavy smoke.
The MS Nordlys, traveling north from Bergen, is one of several ships that ply the Norwegian coast on the popular 1,500-mile (2,500- kilometer) cruise between the southwestern city and Kirkenes, high above the Arctic Circle near the Russian border.
The line carries both tourists eager to see the spectacular western coast and locals from coastal cities and hamlets.