Dozens of people were on board the bus, which was heading from the resort city of Pokhara to Kathmandu on Monday when it drove off the Prithvi highway after midnight, police said.
The bus rolled down a mountain slope and landed on the banks of Trishuli river near Benighat, about 80km west of the capital, Kathmandu.
Among those who died was a 24-year-old British national, according to the Dhading district police office.
Only nine bodies have been identified.
The injured included a Chinese national, who is being treated at the National Trauma Center in Kathmandu, and a 27-year-old woman from New Zealand who received minor injuries and was being treated at a local hospital.
China's official Xinhua News Agency, citing the Chinese embassy in Nepal, reported earlier that one other Chinese national was missing.
Rescuers reached the accident site soon after the accident, and the injured were pulled out of the wreckage and driven to hospitals for treatment, according to government administrator Mohan Prasad Neupane.
Police are investigating the cause of the accident.
Bus accidents in Nepal are common, mostly due to poorly maintained roads and vehicles.
Much of the Himalayan country is covered by mountains and connected only by narrow roads.
The bus landed on the banks of the fast-flowing mountain river.
Two buses with 65 people on board fell into the same river in 2024 and were lost, with most aboard either killed or still missing.
Wreckage of one of the buses was found only in 2026, buried deep in sand.
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