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.
The incident happened shortly after England's Euro 2020 match against Scotland.
A woman and the man, both in their 20s, suffered serious leg injuries and are being treated in hospital.
Their injuries are not believed to be life-threatening, while two other women are also being treated in hospital for less serious injuries.
The driver fled the scene and had not been found by lunchtime on Saturday.
The pub has been closed, the scene sealed off and the Volvo seized for forensic examination.
House-to-house enquiries are continuing and CCTV from around the area is being retrieved, West Midlands Police said.
Neighbourhood officers are also patrolling the area to offer reassurance to residents.
Detective Sergeant Paul Jeffs from Brierley Hill CID, said "This is a serious incident involving both a firearm and a vehicle and four people have been injured.
"We believe that this was a targeted attack and quick-time investigations are being carried out to establish the whereabouts of the driver of the Volvo.
"We would ask anyone who has any information or dash cam from around the time of the incident, and who has not already spoken with officers, to get in touch."
"You can message us via live chat at west-midlands.police.uk, call 101 or speak anonymously to Crimestoppers on 0800 555 111, quoting crime number 20/1029616/21."
A spokesman for Marston's Brewery, which operates the Gigmill, said: "The pub will remain closed while police continue to investigate."
West Midlands Ambulance service has been contacted for a comment.