The pedestrian, in his 30s, suffered injuries not believed to be life-threatening in Shireland Road, Smethwick.
It happened at around 6.30pm on Friday with the force believing two cars were involved in the collision.
A driver of one of the vehicles remained at the scene and she is helping the force with enquiries, whilst the second driver left the scene.
A man in his 60s was arrested on suspicion of causing injury by dangerous driving. He has been released pending further enquiries.
Anyone with information should contact the force, quoting log 3272 of September 30.