The bus which had been carrying tourists had been travelling to the capital, Kathmandu, when it lost control and fell 200m onto the bank of the Trishuli river, in the country's central Dhading district, early on Monday morning.
There were 44 people onboard including the driver, 25 of whom suffered injuries. The bus had been travelling from Pokhara, a popular tourist spot.
Authorities say they are investigating the cause of the incident. The UK Foreign Office has been contacted for comment.