Police say a rescue operation is ongoing to reach casualties and that others are injured after the accident in the Pauri Garhwal district in Uttarakhand, northern India.
At least seven other people are believed to be critically injured.
"People were packed like sardines," said police officer Jagat Ram Joshi.
Trivendra Rawat, the chief minister of Uttarakhand, said the bus skidded and fell into a 700ft (213m) deep gorge.
Senior police official Sanjay Gunjiyal said 20 bodies had so far been pulled out of the wreckage, but that rescue work was being hampered by bad weather.
The cause of the crash is not yet known but Mr Gunjiyal said rain could have caused the bus to skid off the road.
He said: "It is raining (in the area) since morning. Two days back there was a landslide in that area."
Residents were the first on the scene to help the victims, he said.
More than 110,000 people are killed every year on India's deadly roads.
Most crashes are blamed on reckless driving, poorly maintained roads and ageing vehicles. SHARE THIS STORY USING ANY OF THE BUTTON BELOW ⬇ PLACE YOUR TEXT ADVERT BELOW ⬇⬇⬇
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