Rescue workers were searching the fast-flowing waters of the Chenab River for any survivors, said Hemant Lohia.
The accident occurred late Friday in the Kishtwar region, 120 miles (190 kilometers) southeast of Srinagar, the main city in the Indian-controlled portion of Kashmir.
It was not immediately clear how many passengers were traveling on the privately owned bus, or the cause of the crash. Three survivors who managed to climb out and swim ashore said about 20 people were inside, Lohia said.
The minibus was negotiating a curve when the accident happened. "The entire road has been dug up for widening, and it was also slippery because of the rains," Lohia said.
More than 110,000 people die annually nationwide in road accidents, according to police figures. Badly maintained roads, overcrowding and aged vehicles are the cause of a majority of accidents in India.