Search and rescue crews were at the crash site in hilly Pauri Garhwal district northeast of New Delhi, police said.
"44 people have died in the accident. At least three others are injured. The rescue work is still ongoing," disaster management official Deepesh Chandra Kala told AFP.
"The bus lost control and swerved off the road, into a deep valley. It broke into two pieces on impact and it is now in a small river at the bottom of the valley."
Images of the vehicle taken at the scene showed the twisted chassis of a bus with the roof sheared clean off.
Prime Minister Narendra Modi said he was "extremely saddened" by news of the accident and offered his condolences to the families of the dead.
"I pray that those injured recover at the earliest. Rescue operations are underway and authorities are providing all possible assistance at the accident site," the prime minister's office posted on Twitter, attributing the remarks to Modi.
Officials said it was unclear how the accident occurred.
But India has some of the world's deadliest roads and lives are frequently lost in India's mountainous north, where narrow hairpin turns cut paths into the steep Himalayan foothills.
More than 150,000 people are killed in road accidents each year with most deaths blamed on poor roads, badly maintained vehicles and reckless driving.
In April a bus carrying young students home in Himachal Pradesh state plunged into a ravine killing 30 on board, including 27 children.
That same month, at least 21 wedding revellers were killed when their truck flew off a bridge in Madhya Pradesh state.
Days later, 13 children died after a train collided with a small school bus at an unmanned railway crossing in Uttar Pradesh state.
Eyewitness? Submit your stories now via social or:
Email: eyewitness@pulse.ng
