The man was struck by a blue Toyota Auris while he was crossing the road in Farnley at about 1.30pm yesterday.
West Yorkshire Police today said the driver of the car, a 27-year-old man, made off from the scene before returning a short time later.
He was arrested and subsequently released under investigation.
The collision happened while the car was travelling on Butterbowl Drive towards the junction with Whincover Drive.
Police are appealing for witnesses and also want to hear from people who may have dash-cam footage of the Toyota being driven in the area prior to the incident.
Anyone with information is asked to ring West Yorkshire Police on 101, quoting log reference 879 of October 15.