The accident happened near Bhanderkot, a mountainous region about 240 kilometers northeast of Jammu, one of the main cities in Jammu-Kashmir state, said senior police official Haseeb Mughal.
The driver lost control of the vehicle on a sharp curve and the bus plunged about 244 meters into the fast-moving Chenab river, he said.
It was not immediately clear if the bus, which could seat 32, was full.
Mughal said rescue operations were ongoing at the site of the accident.
Deadly road accidents are common in India, often caused by aging vehicles, overloading and reckless driving on poorly maintained roads.