The incident happened on Purneys Road just before 1pm today (November 3).
Emergency services attended and found three men who had been stabbed.
They were taken to a hospital where their conditions are unknown.
At this stage in the investigation, there have been no arrests and enquiries continue.
A crime scene is in place.
A spokesperson for the Metropolitan Police said: “Police were called to Purneys Road, SE9, at 12.55pm on Sunday, November 3, following reports of three men stabbed.
“Officers, London Ambulance Service and London’s Air Ambulance all attended the location.
“Three men were taken to hospital.
“We await an update on their conditions.
“At this stage in the investigation, there have been no arrests and enquiries continue.
“A crime scene is in place.
“Anyone with information that may assist the investigation is asked to call 101 and quote CAD reference 3279/03Nov.
“To remain anonymous please call the independent charity Crimestoppers on 0800 555 111 or visit crimestoppers-uk.org.”