The accident occurred near Khaneri in Rampur, some 140 km from here.
The bus with 35 passengers on board was on its way from Rekong Peo town in Kinnaur district to Nauni in Solan district when it skidded off the road and crashed into the gorge.
Deputy Commissioner Rohan Chand Thakur told IANS that the injured were admitted to nearby hospitals. Some were shifted to the Indira Gandhi Medical College and Hospital in Shimla.
“Most of the dead belonged to Rampur town and its nearby areas,” he added.
The police said the driver of the bus probably lost control over the vehicle while overtaking another bus.
Witnesses said the administration had a tough time extracting the victims from the wreckage of the bus.
Villagers started the rescue operations before the authorities could reach the spot, they said.