The man surrendered to a police station at 10.30am on Wednesday following the incident at the Gigmill pub, in South Road, Stourbridge, on Friday night.
Four people were hurt during the incident, including a man and woman, both in their 20s, who suffered leg fractures and ligament damage respectively.
Two other women were also treated for less serious injuries. All four have now been discharged from hospital, a police spokesman said.
The incident unfolded shortly after the England v Scotlands Euro game on Friday night.
Detectives from West Midlands Police recovered a silver Volvo car at the scene and quickly identified a suspect.
Several arrest attempts were made by officers in the last few days – but the 24-year-old, from the Stourbridge area, handed himself in for questioning on Wednesday morning.
Detective Inspector Chris Fox, from Brierley Hill CID, said: “The man has been arrested for four counts of wounding, plus a firearms offence as a BB gun was discharged during the disorder.
“Two people suffered nasty leg injuries but thankfully no one was critically injured.
"This was a very serious incident, which we believe was a targeted attack, that could have had tragic consequences.
"We have examined CCTV and spoken to several witnesses but if anyone saw what happened and has not yet spoken to us then please get in touch.”
Anyone with information is urged to call West Midlands Police on 101, quoting crime number 20/1029616/21.
Alternatively, call Crimestoppers anonymously on 0800 555 111.