Officers were called to Rye Lane last Thursday (December 5) at 10.27pm and found a man who was stabbed in the neck and thigh.
The injuries were originally described as life-threatening, but he has since been discharged from hospital.
Now an appeal has been shared by police to find the suspect, described as a black man, around 5ft 4inches and in his 40s.
While no images have been released, he is said to have a stocky build and a short beard.
At the time the suspect wore a black jacket with wording print on it.
Detective Constable, Jacob Ludlam, from the local investigations team, said: “We are urging anyone who may have been in Peckham Rye that evening to please think back and let us know if you saw or heard anything suspicious.
“Whilst our enquiries are ongoing, it appears at this stage to be an unprovoked attack.
“The incident occurred opposite John The Unicorn pub, so if you were there that night or knew anyone that was, please get in touch with us online or call 101 quoting reference 01/1168928/24.”
“Alternatively you can report it to the independent charity Crimestoppers anonymously on 0800 555 111.
“Any snippets of information could be vital to our investigation. Thank you.”