The 42-year-old man was ta had suffered minor head, neck and back injuries, a police spokesman said.
Emergency services were first called to Water Lane in Holbeck at around 6.45am after the wagon collided with a bridge.
It is thought items in a skip on the back caught the bridge as the wagon tried to pass underneath.
The police spokesman said officers on the ground had advised closing the road until wagon could be recovered.
It has now been towed away and debris from the collision has also been recovered by the company which owns the wagon.