The car was driven towards the Gigmill pub on South Road in Norton, Stourbridge, injuring a man and three women at around 10pm on Friday.
The driver of the silver Volvo is understood to have got out of the vehicle and fired shots from a BB gun, hitting the man in the leg causing a minor injury.
He then drove the car towards a group standing on steps outside the pub before fleeing the scene and has still not been found.
A woman and the man, both in their 20s, suffered serious leg injuries in the incident and were taken to hospital.
Their injuries are not believed to be life-threatening, West Midlands Police said, while two other women were also being treated in hospital for less serious injuries.
The pub was busy on Friday evening, with the shooting happening shortly after England's Euro 2020 draw with Scotland.
The Marston's pub was closed on Saturday but back open as normal for Father's Day on Sunday.
Anyone with information is asked to contact police quoting crime number 20/1029616/21.