The 54-year-old, who was involved in an altercation with a white van driver on the A8, in Renfrewshire, died in hospital at the weekend.
It is understood he may have been suffering from a head injury.
Police today appealed for help in trying to piece together what happened.
The incident happened on the A8 near to Langbank at around 2pm on July 7.
Police said the man was driving a black Ford Mondeo westbound, when he became involved in an altercation with the driver of a Ford Transit van.
Both vehicles stopped and the Mondeo driver got out of his car to speak with the other driver.
The man, whose identity has not yet been released, was treated for "minor injuries" at the time and released from hospital later that day.
However, on Thursday he was re-admitted to the Royal Alexandra Hospital and he died on Saturday.
A post-mortem examination is due to take place.
Police believe motorists, who were travelling on the road at the time of the altercation, may hold the key to solving the mysterious death.
Officers have appealed to drivers who may have seen the two vehicles stopped at the side of the road to come forward.
A spokeswoman for Strathclyde Police said: "Officers are working to establish exactly what took place and we would ask any witnesses, or anyone with any information on the incident, to contact police."
Anyone with any information about the incident is asked to contact the Divisional Road Policing Unit at Greenock Police Station on 01475 492661 or 01475 492537.