A 24-year-old man from Sandown was unloading his car at Seaview Esplanade when another vehicle was driven over his left leg.
The car is believed to have been a black hatchback. It is reported that the driver did not stop at the scene.
The man was treated in hospital for a serious leg injury which was not life threatening.
Investigating officer, PC Nigel Gore, said: "We are appealing for the driver of a black hatchback vehicle which failed to stop after colliding with a man's leg to contact us.
"It is possible the driver did not realise a collision had occurred which is why they did not stop at the scene.
"This collision took place on Wednesday, August 22 at around 12pm.
"We would also like to hear from witnesses as they may be able to identify the vehicle and driver involved."
Anyone with information is asked to contact PC Nigel Gore at Shanklin police station by phoning 101.
Information can also be given anonymously by phoning the Crimestoppers charity on 0800 555 111