Police were called to Balham High Street on Sunday, August 24 to reports of the assault.
A man in his 60s was found at the scene and taken to hospital with life-threatening injuries.
He later died from his injuries on Friday, September 5.
Two people – a man aged 37 and a woman aged 30 – were arrested on the same day, the first on suspicion of murder and the second for conspiracy to commit murder.
They both remain in custody for questioning.
Police enquiries continue.
Detective Chief Inspector Matthew Denby from the South-West Specialist Crime team, said: “This is an incredibly sad incident where a 67-year-old man has lost his life after being seriously assaulted following a dispute in the street.
“We are working at pace on what is now a murder investigation.
“Were you in the area or on Balham High Road on Sunday, 24 August? If so, we really need your help.
“If you have any mobile phone or dash cam footage from the area around the time of the incident, please send it to police. It could be critical evidence.”
Witnesses or anyone with any information is asked to call 101 or post on X ‘@MetCC’ quoting CAD 4647/24Aug.