The incident happened near The Greyhound pub in Kirkdale at 4.15am yesterday (April 27).
Officers and London Ambulance Service crews attended and found a man who had been stabbed.
He was taken to hospital for treatment where his injuries were assessed as non-life threatening.
No arrests have been made as police enquiries are ongoing.
A spokesperson for Metropolitan Police said: “On Sunday, 27 April police were flagged down by a member of the public at 4.15am in Kirkdale, SE26 after a man was stabbed.
“Met officers alongside paramedics from the London Ambulance Service treated a 39-year-old man for stab wounds, before he was taken to hospital where his injuries were confirmed to be non-life threatening or changing.
“At this early stage, there have been no arrests, an investigation has been launched into the circumstances.
“If you saw or have any information that may assist police then please call 101 stating CAD1223/27APR or alternatively call Crimestoppers on 0800 555 111 to remain anonymous.”
A spokesperson for London Ambulance Service said: “We were called at 4.16am on Sunday 27 April to reports of an incident on Kirkdale, SE26.
“We sent resources to the scene, including an ambulance crew, an incident response officer, a paramedic in a fast response car and a clinical team manager.
“We treated a man at the scene and took him to a major trauma centre as a priority.”
