The incident occurred when the bus, headed towards Gwalior skidded off on a turn and plunged into the drain which is around 20 feet beneath the bridge, SP M L Chhari told PTI.
He said the driver lost control over the vehicle after one of its wheels landed in a crater near a turning on the bridge.
"The bus broke the railings of the bridge and fell into the drain, killing five persons and injuring 26 others," Chhari said.
While four out of the five deceased, identified as Nasir Khan (35), Kaliya Gujjar (23), Monu Gujjar (25) and Lalaram (42), died on the spot, Ramhat Gujjar (26) succumbed to his injuries at the hospital.