The 72-year-old was standing outside of his car in Strathcona Gardens around 1.25pm when he reached in to start the engine.
The vehicle, a Honda Accord, started moving causing the man to fall onto the pathway.
Police and an ambulance attended and the injured man was taken by ambulance to the Queen Elizabeth University Hospital but later died.
Sergeant Craig Beaver from the Road Policing Department at Helen Street is appealing for information.
He said: “A number of people came to assist the injured man during this incident, however some of them had left on police arrival and I would ask any witnesses who have not yet spoken to officers to please contact us.
“I would ask anyone with information that may assist our ongoing enquiries to contact the Road Policing Department at Helen Street through 101 quoting reference number 1961 of 15th May 2019.”