The fire also injured nine others and forced more than 200 passengers to evacuate the ship, with more than 100 passengers piling into lifeboats in the frigid waters.
The rest of the passengers were evacuated at a dock in Aalesund, 230 miles northwest of the capital of Oslo.
"Nothing indicates sabotage or points to terror," said Trygve Oedegaard, head of operations at the Aalesund police.
Police say they suspect an explosion started the fire in the engine room. The ship was traveling from Bergen to Kirkenes when the fire started.
Thick black smoke billowed from the stern of the boat, the MS Nordlys, of Norway's Hurtigruten line even before it pulled into the dock.
The Associated Press contributed to this report.