The incident happened outside Peckham Library on Peckham Hill Street just before 6.40pm on Wednesday, November 5.
Officers and London Ambulance Service crews attended and found a 26-year-old man who had been shot.
He was treated at the scene before being taken to hospital.
Police confirmed today (November 9) that his injuries are not believed to be life-threatening.
There has been no arrests at this stage and enquiries are ongoing.
People in the area of a shooting in Peckham initially thought the gunshot was fireworks.
May was working nearby at an internet cafe on Peckham High Street when she heard three or four popping sounds at around 6.45pm.
She said: “It was quite loud. I thought it was fireworks. And then when I went outside they said, shooting.
“I just heard popping and then while I was sweeping police were covering the area with tape.
“I thought it was a stabbing, because stabbings are usually happening.”
