The incident took place at about 03:15 on Saturday outside the EQHQ nightclub in Livingston.
The vehicle then drove away from the scene.
A 23-year-old man was arrested by police a short time later. He is expected to appear at Livingston Sheriff Court on Monday.
The 22-year-old was taken to hospital for treatment but his injuries were not believed to be life threatening.
Det Insp Paul Batten said: "Fortunately the victim was not fatally injured as a result of this collision and we are continuing with our inquiries to establish exactly what happened.
"We know that there were a number of people in the area, including patrons from the ECHQ and customers at nearby eateries who may have witnessed the incident or have information that can assist with our investigation.
"These individuals are asked to contact police immediately."
A man has been charged with drink-driving after a 22-year-old man was struck by a car as he left a nightclub in West Lothian.