Police officer S.P. Vaid said the bus swerved off a mountain road, but the cause of the accident was not immediately clear.
A police statement said 27 injured, 19 in critical condition, were taken to hospitals in Banihal, a town 120 kilometers (75 miles) south of Srinagar, the main city in Indian-held Kashmir.
Police said it had rained in the area, making the road slippery. Some landslides caused a heavy traffic jam on the main highway linking Srinagar with the rest of India.
Police figures show India has the world’s deadliest roads, with more than 110,000 people killed each year in crashes. Driver fatigue and negligence, low-quality roads and poor vehicle maintenance are the usual causes of such accidents in India.