The Himachal Road Transport Corporation bus from Shimla met with the accident near Kandaghat on the Kalka-Shimla national highway at around 12:15 pm, police said.
A rescue and relief team was rushed to the accident site to shift the injured to hospitals and extricate the bodies of the victims, they said.
They said senior police and administrative officials along with Chief Minister Virbhadra Singh, who is touring the area, supervised the operation.
The seriously injured were being brought to Indira Gandhi Medical College hospital in Shimla while the others had been admitted to Kandaghat and Solan hospitals.
The chief minister has expressed shock over the accident and asked the district administration to provide all possible help to the victims.