Deputy Administration Commissioner Sunil Chaudhary said the bus was on its way to Chamba in Himachal Pradesh state when the driver apparently lost control of the vehicle, the Hindustan Times reported. Witnesses said the bus was overcrowded and passengers were sitting on the roof.
Two children and 18 women were among the dead. The Times said many of the passengers were on their way to a fair in Chamba.
Kuldeep Sharma, the police superintendent in Chamba, said at least 10 of the injured were in critical condition.
Himachal Pradesh is in the western Himalayas.