The driver lost control of the vehicle due to excessive speed on Monday afternoon, said Alamgir Hossain, chief of Padma Bridge North Police Station.
Army personnel, who were patrolling the area, rescued the injured and took them to Sreenagar Upazila Health Complex.
Normal traffic resumed after police removed the vehicles from the road.
He said the truck flipped after hitting the railings of the approach road. Onions from the truck spread on the road at that time.
Authorities banned motorcycles from the bridge later and launched a mobile court drive to prevent people from stopping their cars on the bridge.