The incident happened in Hither Green Lane near Benin Street at around 3.25pm today (October 28).
Officers and London Ambulance Service crews attended and found a man who had been stabbed.
He was taken to hospital for treatment where he died shortly after.
The man’s next of kin have been informed and are being supported by specialist officers.
Formal identification and a post-mortem examination will take place in due course.
Superintendent Nick Jowett, of the Met’s Royal Borough of Greenwich Policing team said: “Our thoughts are with the victim’s family at this distressing time.
“Although we are in the very early stages of the investigation, I can assure you that detectives are working at pace to identify those responsible for this senseless attack.
“In the meantime, local residents can expect to see an increased police presence across the area.
“Please speak to them if you have any concerns.”
There have been no arrests at this early stage.
Those with information relating to the incident are urged to share it via 101, quoting 4648/28OCT.
Hither Green Lane and Benin Street are closed while a crime scene remains in place.