The incident occurred shortly before 8.00pm at the cityside end of the bridge.
The rescued man was taken by ambulance to Altnagelvin Hospital.
It is understood he did not sustain any serious injuries.
A spokesperson for Foyle Search and Rescue said volunteers in two boats were tasked to the scene but were “stood down” prior to arriving.
The spokesperson added: “The male who helped in the rescue tonight is not a volunteer with Foyle Search and Rescue.”