The Derry charity confirmed that at 11.32pm on Monday night, the Police Service of Northern Ireland tasked its Emergency Response Team to initial reports of a person having entered the water.
A mobile Unit, two boats and crew plus a jet ski responded, with a support team back at base.
A spokesperson said: “Two persons were observed on the riverbank with one prioritised and safely extracted to FSR Boat with support from jet ski and Emergency Response Coordinator on land.
“The person was then transferred to Hospital from our Prehen Base.
“All FSR teams were then debriefed and off water at 00:40hrs Tuesday March 9. Appreciation to PSNI, CCTV and the community group involved.”
The spokesperson added: “Foyle Search & Rescue would advise that under no circumstances should anyone cross over railings to enter the glar/mud or water to attempt a rescue.
“You may get into difficulties and also require our help, Also please wear the appropriate PPE, personal protective equipment.
“If you need support and help please don’t do it alone, reach out. Please find some useful contact numbers below.