The London Ambulance Service was called to Winslade Way, near Catford Mews, at around 7.30pm on Monday (October 21).
A man was treated at the scene and taken to hospital “as a priority”.
His condition is not yet known, and no arrests have been made.
A police cordon was seen outside the Iceland store in Catford Mews following the incident.
Superintendent Charlene Pavitt, who leads policing in Lewisham, said she understood the recent violence had caused concern among residents.
She 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.”
It is the fourth stabbing in a week in Catford since October 15, when a man was stabbed to death on nearby Rushey Green.
Later that day a second man was stabbed in Mountsfield Park.
Police have been 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.
According to the latest updates from police, there have been no arrests in relation to any of these incidents.