The incident happened at 7.30am near the municipal market at the Paphos town centre.
At some point Ioannis Michail had one leg outside the car when the vehicle rolled backwards and caused him to fall to the ground.
He was rushed to hospital where he was diagnosed with fractured ribs but he later succumbed.
Police said they were investigating the incident.
The exact cause of death is expected to be determined by a postmortem.