Eight bodies have been recovered, Superintendent of Police Sumedha Diwedi told IANS on phone.
She said the bus, ferrying passengers from Punardhar to Solan town, met with the accident just five km into its journey from the starting point.
Official sources said the toll could be higher.
The accident spot in Sangrah tehsil is some 130 km from district headquarters Nahan.
Sirmaur is one of remotest places in the state. Buses plying there have poor frequency, and the scarcity of means of transport often leads of overcrowding of vehicles.