The incident happened just after 9pm on Sunday, January 21, in the small car park outside the Bench Road shop.
A 29-year-old man suffered injuries to his face, arms and ribs and was later taken to hospital for treatment.
The car did not stop at the scene.
Police are appealing for information from anyone who was in the area and may have witnessed the collision or seen the car driving off.
Derbyshire Constabulary believes a couple were near the car park when the incident took place and the force is keen to trace them.
Anyone with information should call Derbyshire police on 101 quoting reference 18000033221 or Crimestoppers on 0800 555 111.