The maritime rescue service said the Viking Sky, with about 1,300 passengers and crew on board, had sent out a mayday signal as it had been drifting towards land.
The crew were later able to restart one engine and the ship was at anchor about 2km from land and the passengers were considered safe although the evacuation was set to continue, the rescue service said.
Only 87 people had been evacuated by 1750 GMT, and the airlift was set to continue throughout the night, rescue service spokeswoman Borghild Eldoen said. Eight of those evacuated had suffered light injuries.
Passengers were hoisted one-by-one from the deck of the vessel and airlifted to a village just north of the town of Molde on Norway’s west coast.
A second vessel, a freighter with a crew of nine, was also being evacuated nearby after suffering engine failure.