The bus carrying 56 people swerved off the road and fell into the Tons river, officials said. They said the toll could rise, reports the BBC.
Rescue teams have reached the scene and recovery operations are under way.
Road accidents are common in India, often due to poor driving or badly maintained roads and vehicles.
The privately-operated bus was travelling from a small town in the neighbouring state of Uttarakhand.
India has the highest number of road fatalities in the world; more than 400 people are killed in accidents every day.