Police were called to Effra Parade at 8.17pm on Wednesday, 2 June after being alerted to a stabbing by the London Ambulance Service.
Officers attended with paramedics and found a 20-year-old man with a stab wound to the leg.
He was taken to a south London hospital where his condition was assessed as non-life threatening. He has since been discharged.
There have been no arrests but an investigation is under way.
Officers believe the stabbing took place in Brockwell Park, a short distance away from where the man was found. They are appealing for anyone who may have been in the park and witnessed the incident, or who has other information about what happened, to come forward.
In particular, they are keen to identify and speak to a man who was seen in the area earlier in the evening. He is described as black, around 5ft11, with a large build, wearing a grey tracksuit and white top with grey writing on.
Detective Constable Kismet Green, who is leading the investigation, said: “We are keen to speak to anyone who was in the Brockwell Park area on Wednesday evening at around 20:00hrs.
“The park was busy because of the warm weather and we believe there will be people who witnessed the incident or noticed some sort of altercation.
“We would encourage anyone who knows anything, no matter how small, to get in touch.”
Anyone with information should call 101, providing the reference CAD7355/02JUN.
Information can also be provided to Crimestoppers, anonymously, on 0800 555 111.
Hard calls save lives. Are you close to someone on the fringes of knife crime? Do the right thing, please give information, 100 per cent anonymously, through the independent charity Crimestoppers. No piece of information about knife crime is insignificant or too small. Any information you give to Crimestoppers can make a difference in reducing knife crime and the harm it causes to families.