Norway's sea rescue agency said the MV Viking Sky sent out a distress signal and was drifting towards the shore.
Helicopters and rescue boats are at the scene in high waves and strong winds.
One person at the scene told the newspaper that the waves are several meters high.
Police customs the newspaper VG winds are blowing at 38 knots, and the ship is less than 2.5 nautical miles (4.6 km) from the shore
However, reports suggest the ship has managed to restart one engine and move slightly further from the coast as the evacuation continues
MV Viking Sky is a Viking Ocean Cruises ship, which had its maiden voyage in 2017
Website MarineTraffic shows the vessel was en route to Stavanger from Tromso, and is drifting off the town of Farstad near Molde on the country's western coast.
The company website shows it has capacity for 930 guests on board. 19659007] The area is known as the Hustadvika and is reportedly one of the most dangerous stretches of Norway's coast.