Officers were called at approx. 18:55hrs on Thursday 25 October to Fulham High Street, SW6 following reports of an assault.
London Ambulance Service and London's Air Ambulance also attended and discovered a man, aged 65, suffering from stab wounds. He was pronounced dead at the scene at 19:36hrs.
Next of kin are in the process of being informed, formal identification awaits. A post mortem will be scheduled in due course.
Detective Inspector Craig Bradley of the Homicide and Serious Crime Command leads the investigation. He said:
"I am appealing for any people who were in the area and witnessed this incident, or the events leading up to this incident, to come forward and speak to my team.Anyone with information is asked to contact the incident room on 0208 345 3715 or call Crimestoppers anonymously on 0800 555 111.
"At this early stage it is unclear what the motive for this incident was - if you saw anything, or have any information which may help the investigation, please get in contact."
A man, aged 27, was arrested near the scene on suspicion of murder - he remains in custody at a west London police station.