Officer Clayton Lewis was grazed in the leg during the exchange of fire.
The suspect Tadarius Hunt was pronounced dead at a local hospital. Hunt was wanted in connection with the shooting of a worker at the Nashville Rescue Mission, police said in a video .
The incident on the bridge began when an officer spotted Hunt and ordered the man to stop and come to him.
Hunt ran away until he was intercepted from the other direction by Officer Lewis.
Dashcam video from the incident shows Hunt attempting to escape from Officer Lewis, producing a weapon, and firing. The officer returned fire.