The woman, in her 20s, was seriously injured when she was reportedly hit by the vehicle in Whitehawk Crescent, Brighton.
A 26-year-old man was arrested on suspicion of causing serious injury by dangerous driving at the scene of the incident and remains in custody.
The man was also arrested on suspicion of intentional strangulation, driving whilst unfit through drink and assaulting an emergency worker.
Following the incident at around 6am this morning, a Sussex Police spokeswoman said that the road remained closed while officers continued to investigate.
Sussex Police added: “Anyone who saw what happened or has any other information, including relevant CCTV, doorbell or dash cam footage, is asked to contact police online or by calling 101 quoting Operation Bromley.”