Among those killed were a British, Chinese and Indian citizen. The bus was carrying 44 passengers.
A New Zealander and a Chinese national were among 25 injured when the bus heading for Kathmandu from the tourist town of Pokhara fell from the road at Behighat in Dhading District, 80 km (50 miles) west of the capital, a police statement said.
The injured are being treated at hospitals in Kathmandu, it added.
Road accidents are common in mostly mountainous Nepal where the conditions of roads are poor. Hundreds die in road crashes in Nepal annually.
The government said it had ordered an investigation.