Police were called to a report of a stabbing at what they described as a multi-occupancy address in Ringstead Road, Catford at 4am on Sunday.
The victim was taken to hospital, where he was pronounced dead at 5.29am.
He has not been formally identified, although police are in the process of informing next of kin.
A post-mortem will take place in due course, police said.
No arrests have been made so far, Scotland Yard said, with the Homicide and Major Crime Command leading the murder investigation.
Anyone with information can contact police on 101 quoting CAD1274/18AUG or Crimestoppers anonymously on 0800 555 111. You can also tweet @MetCC.