Officers were called to reports of a disorder on the car park of Halfords on Coventry Road, Sheldon.
They found a 20-year-old just before midnight on Friday under a white WV Golf, after having apparently been run over.
The man suffered serious head injuries and was pronounced dead a short time later, a spokesman for the force said.
Members of the public detained a 25-year-old man at the scene and he was then arrested on suspicion of murder.
Officers will be at the scene today as investigations continue – with CCTV also being recovered.
Anyone with information has been asked to get in touch, quoting log 4720 of 9 April.
Alternatively, contact Crimestoppers anonymously on 0800 555 111.