The Kathmandu-bound bus had left Khotang district in the morning, and was said to be overcrowded.
The vehicle rolled down the road at Barkhetar of Arkhanle in the district.
The wreckage was trapped between trees, making it difficult to rescue survivors. It took hours for the first rescuers to reach the site because of the location.
The identities of the deceased are yet to be established.
Thirty one people have been rescued alive, said police and added that the injured have been admitted to a hospital.
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Reports said an army rescue helicopter was headed to the crash site.
Nepal is mostly covered with mountains and most roads are narrow. Bus accidents in the country are generally blamed on poor roads.
Buses are usually crowded and people often travel on the roofs.