Officers said the collision took place on Monday (24 February) around 18:50.
They said the blue Audi Sport was travelling from St. Aubin up Le Mont Le Vaux, and then continued onto La Grande Route de St. Brelade.
Shortly before the bend, it reportedly overtook a car and cyclist before hitting the wall by the Mont Arthur junction.
Police are now looking to hear from witnesses. In particular, they wish to make contact with the cyclist they briefly spoke to at the time.
Anyone with more information is urged to call 612612 or make an anonymous report via Crimestoppers.