The 35-year-old man, who has not been named, was walking on Coopers Green Road in Uckfield at about 01:00 GMT on Saturday.
A vehicle believed to have been involved was later traced by police to a nearby address.
A 26-year-old man was subsequently arrested on suspicion of causing death by dangerous driving. He has been released on bail until 28 February.
A pedestrian has been struck and killed by a car in Sussex.