Only two people, including the ticket checker, survived the crash, according to Rohan Chand Thakur, the district magistrate of Shimla district.
Thakur said the bus fell into a 200m deep gorge on the Tons River. The cause of the accident wasn't immediately clear.
He said that rescue teams were working to recover the wreckage from the gorge.
Driver fatigue, negligence, poor quality roads and vehicle maintenance are the usual causes of such accidents in India.
Police figures show India has the world's highest road accident death toll, with more than 110 000 people dying each year in crashes.