Police were called at 7.48am on Thursday, 21 October to Sandy Hill Road, SE18 to a man collapsed in the street.
London Ambulance Service attended and the man, aged in his 20s, was pronounced dead at the scene.
A crime scene remains in place.
The victim’s next of kin have been made aware and are being supported by specialist officers.
The investigation is being led by Detective Chief Inspector Richard Leonard, from the Met’s Specialist Crime Command. He said: “Sandy Hill Road is a residential area and I would ask anyone who was in that area early on Thursday morning to get in touch with us if you saw anything unusual or out of place.
“Similarly, please check any doorbell or dashcam footage in case you have captured something that could prove useful for our investigation. No piece of information is too small.”
Detective Chief Superintendent Trevor Lawry, in charge of policing for Greenwich, Lewisham and Bexley, said: “My thoughts are first and foremost with the victim’s family who are now having to come to terms with losing their loved one.
“We understand the shock this will cause in the community and we are here to listen to your concerns. I would encourage people to speak to their local officers and ask any questions they may have.
“I will also be meeting with partners and community representatives to discuss the incident and how we can continue to work together to prevent serious violence.”
There have been no arrests at this stage. To provide information, call the incident room on 0208 721 4622.
To remain completely anonymous phone Crimestoppers on 0800 555 111.