Police were called to Winslade Way in the Catford Centre at around 7.45pm yesterday (October 21).
Officers arrived with paramedics who treated the victim for stab wounds.
He was taken to hospital where his injuries have been confirmed to be non-life threatening or changing.
LIVE updates as police tape off busy shopping centre in Catford after stabbing
There have been no arrests and a crime scene was put in place near Iceland.
It is the fourth stabbing in a week in Catford since October 15, when 27-year-old Sanchini Thompson was stabbed to death on Rushey Green at around 3am.
Later that day a second man was stabbed in Mountsfield Park with police unable to confirm the severity of his condition.
On Monday (October 20) a teenage boy was stabbed on Canadian Avenue.
His injuries are not life-changing or threatening.
There have been no arrests in relation to any of the stabbings.
Local police chiefs have stressed they are not connected and are isolated incidents.
Superintendent Charlene Pavitt, who leads policing in Lewisham, has said: “I understand that this is the fourth knife related incident to take place in Catford in the past week.
“This is understandably going to cause concern within the community.
“I have ensured that officers are on the ground, patrolling hotspot areas, to keep the community safe.
“I can confirm that none of the incidents are connected.
“They are isolated, and do not pose a threat to the wider public.
“Active enquiries remain on-going into each incident, including searching for those responsible.
“If you have any information that can assist police, then please do come forward.”
If you have any information, call 101 stating CAD6958/21Oct. Alternatively, you can call Crimestoppers on 0800 555 111 to remain anonymous.
