About 700 people had been evacuated from the area as of Wednesday evening local time.
“There were two massive tremors that lasted for a long while and I assumed it was snow being cleared or something like that,” Oeystein Gjerdrum, 68, told broadcaster NRK.
“Then the power suddenly went out, and a neighbour came to the door and said we needed to evacuate, so I woke up my three grandchildren and told them to get dressed quickly.”
The missing people were from homes in the innermost area of the landslide but it was not clear whether they had been trapped in their houses, were away at the time or had managed to escape, the police said.
“It is a catastrophe,” Prime Minister Erna Solberg told reporters after visiting the site. “There could be people trapped, but at the same time we can’t be sure because it is the New Year’s holiday which means people could be elsewhere.”
She warned that rescue operations could take a long time.
“This could take days,” she said. “The situation is still so unstable that it is impossible to do any (rescue) effort other than from helicopters.”
The area remains unstable for now and can only be accessed by helicopter, said Roger Pettersen, head of the police operation at the site.
Masses of earth were still moving in what has been one of the largest clay slides in recent Norwegian history, Torild Hofshagen, the regional head of the Norwegian Water Resources and Energy Directorate, told a news conference.