The incident took place as the bus with 85 passengers, heading for Kattike Deurali from Kathmandu, skidded off the road at Birta Deurali-7 in Kavre.
District Chief of the National Investigation Department Dhan Bahadur Budhathoki said 31 bodies have been recovered and the death toll may rise further.
A Nepal Army helicopter airlifted 15 injured passengers to Kathmandu for treatment, according to the Ministry of Foreign Affairs. An eyewitness said that many passengers have been squeezed by the bus wreckage.
Prime Minister Prachanda directed concerned stakeholders including the government bodies to intensify rescue mission.
Nepal is mostly covered with mountains, and most roads are narrow. Most accidents in Nepal are blamed on poorly maintained vehicles and road conditions. Buses are crowded and people also travel on the roofs of buses.