The driver lost control of the vehicle at a sharp bend on a mountain road in Himachal Pradesh state, nearly 385 miles north of New Delhi, police officer Raj Kumar said.
The bus then plunged more than 300 feet into the gorge, Kumar said.
Twenty other people injured in the accident have been hospitalized, the Press Trust of India news agency said.
Kumar said the rescue operation was continuing and that the death toll of 39 was likely to rise.
Police figures show India has the world's highest road death toll, with more than 110,000 people dying each year in accidents commonly caused by overcrowding, speeding, and poor vehicle and road maintenance.
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