"Two people from the ship are dead," Borghild Eldoeen, a spokeswoman for the rescue service centre in southern Norway, told AFP.
"Twelve are injured but we don't know how serious" their injuries are, she said.
The Aalesund hospital said it had admitted nine patients from the fire, including two who were seriously injured.
"Those in serious condition have burns and are probably suffering from smoke inhalation as well," it said on its website.
The Nordlys, one of the Hurtigruten company's coastal cruisers, was at sea off the southwestern city of Aalesund when the blaze broke out and was quickly escorted to port.
There were 262 people aboard the ship, almost all of whom were evacuated. A few remained on board to help battle the blaze with firefighters.
"The fire is under control now but we have a problem with the ship taking in water so right now they are working on stabilising the vessel," Eldoeen said.
The ship was in harbour "so the conditions are good for the work."
Big clouds of black smoke had earlier been seen billowing out of the docked ship as rescue crews evacuated the passengers and fire fighters battled the blaze.
There was no specific information about the nationalities of those aboard, but most of the tourists on the Hurtigruten ships are from Norway, though there are often foreigners as well.