Police said the incident happened at the junction of Beverley Road and Eldon Grove at 03:45 GMT.
A BMW car hit the four people before coming to a stop. All the pedestrians were hurt, with one suffering serious injuries, police said.
A man has been arrested on suspicion of dangerous driving as well as driving while under the influence of drink or drugs.
Four pedestrians were injured as they were hit by a car in a Hull street.