The micro-bus carrying 17 people fell some 150 metres down the road while negotiating a sharp bend, police said.
Seven of the 10 killed have been identified so far. One of those identified is Indian national Fida Hussain while the six others are Nepalese, they said.
Five other people were injured in the accident that took place in Chhatiban village in Doti district, police said.
The accident site lies on Nepal-India border, some 700 km west of Kathmandu.
The ill-fated bus was heading towards Mahendranagar from Dadeldhura in the far-west Nepal, police said.