A majority of the tourists were from Saharanpur in Uttar Pradesh.
Officials said the toll could increase as some more passengers might be trapped in the bus wreckage.
The bus carried around 60 tourists and was on its way from Renuka to Paonta Sahib in the hill state.
It met with the accident near Madhara Ghat, some 15 km from Renuka and 50 km from district headquarters Nahan, Assistant Superintendent of Police BS Thakur told IANS.
the bus skidded off and fell into a gorge in Himachal's Siramur district
The cause of the accident is yet to be ascertained, he said over phone from the spot.
The injured were admitted to government hospitals in Nahan, Paonta Sahib and Dadhau.
Witnesses said police had a tough time extricating the bodies from the mangled steel of the bus.
Chief Minister Virbhadra Singh expressed shock and grief over the accident and directed the district administration to take all possible measures to rescue the victims and provide them adequate relief.