"Nothing can be said about the exact number of dead...the picture will be clear in a few hours," said Transport Minister Jai Narayan.
The bus, owned by a state transportation company, was believed to be carrying 61 passengers, mainly school pupils. Witnesses say the bus suddenly veered off the bridge, smashed through a safety barrier, and plunged into the seven-meter (23-foot) deep canal.
Four children managed to swim to safety, and were rushed to hospital in a critical condition. A total of 20 divers were brought in for the rescue operation. Rescue efforts are being hampered by the strong current, and authorities have stopped water entering the canal through a nearby dam.
Five adult bodies, including that of the driver, have so far been fished out of the water.
The cause of the accident is currently being established, but eyewitnesses say the driver probably lost control due to excessive speed. The bus was the only vehicle on the bridge at the time of the tragedy.
Poor road conditions, ageing vehicles and reckless driving are the leading causes of road deaths in the country. Last December, at least 18 people, many of them children, died in the northern Indian state of Punjab when a passenger train collided with a school bus in thick fog. Railway officials blamed the bus driver, saying that the crossing gate was closed.
