The Kia Sportage vehicle moved as the pensioner returned from a walk in Bolton, Greater Manchester, on Saturday.
Emergency services attended the scene, at the junction of Crompton Way and Crompton Vale, at about 2.20pm, but the the man was pronounced dead.
Sergeant Philip Shaw, of Greater Manchester Police's serious collision investigation unit, said: "This appears to be a tragic accident and our thoughts are with this man's family at this terribly difficult time for them.
"It remains important that we conduct an investigation into the circumstances of this incident to make sure the family have answers to why this happened.
"We encourage anyone who witnessed the incident, saw the car prior to the man's return to it, or has any information that may assist our inquiries to get in touch."
Anyone with information can contact police on 0161 856 4741 or the independent charity Crimestoppers, anonymously, on 0800 555 111.