As per reports, all the pilgrims belonged to Indore. Madhya Pradesh, and were returning from Gangotri shrine.
The accident occurred at around 6 PM when the bus fell 300 metre down the road into the river, Dharasu police station incharge Ravindra Saha said.
Twenty one bodies have been recovered so far while the rescue efforts are still on. The casualties may rise as some bodies may still be trapped in the mangled remains of the bus.
There were around 29 pilgrims, mostly from Indore, in the bus at the time of the accident.
The persons, who are injured in the mishap, have been admitted to the district hospitals in Uttarkashi and Chinyalisaur, Uttarkashi District Magistrate Ashish Shrivastava said.
Madhya Pradesh Chief Minister Shivraj Singh Chouhan announced an ex-gratia of Rs 2 lakh each to the next of kin of the deceased.
The bus was ferrying 'Chardham' pilgrims from Gangotri in the Himalayas to Haridwar from where they had to go to Kedarnath.
Rescue operations are being carried out with the help of ITBP, SDRF and police personnel but they are facing difficulties due to the dark, he said.