Police Scotland confirmed a man died following the incident on the corner of Biggar Road and Frogstone Road West, in the Fairmilehead area at around 4.30pm on Thursday afternoon.
Officers said that two men, both driving vehicles, were involved in a dispute before the 69-year-old man collapsed.
A local shop worker said there had been an issue between the drivers from the roundabout further down the road, and that he saw the two men jump out of their vehicles and have a "shouting match" before the older man "turned purple and collapsed."
The worker said that people left their cars and bikes to try and help the man, with CPR being administered.
The man was then taken to the Edinburgh Royal Infirmary where he later died.
A Police Scotland spokesman said: "We were called at about 4.30pm yesterday at Biggar Road where a 69-year-old man took unwell and collapsed after a dispute between him and another male driver of a car.
"He was taken to the Edinburgh Royal Infirmary where he died. Enquiries are ongoing into this incident."
The road was closed for around four hours following the incident before being reopened at around 8.30pm.
Local councillor Scott Arthur said: "This is appalling news from just five minutes walk from my home - my thoughts are very much with the family of gentleman.
"We must wait to fully understand what happened here, but this incident will only add to the calls from local residents to make this road safer for drivers, cyclists and pedestrians, and that must start by reducing the speed limit."