The two men were shot near City Hospital in Western Road at around 5.30pm on Tuesday, April 13.
A 31-year-old man died from his injuries, while the other victim, 22, remains in hospital in a critical condition.
A 29-year-old man has been arrested on suspicion of conspiracy to commit murder and was in custody on Wednesday afternoon.
Detective Chief Inspector Ian Ingram, from West Midlands Police's homicide team, said: “The events of last night are shocking and very sad.
“A young man has died and another is very poorly after being seriously injured.
“There is no place for violence like this on our streets and we’re doing all we can to establish what happened yesterday evening and why.
“I would encourage anyone who may have seen something, or anyone who knows anything about what happened to get in touch with us as soon as possible.
“We are supporting the family of the man who has died and officers are continuing the forensic examination of the scene, a CCTV trawl and other enquiries.”
Hours later a 16-year-old was shot in the arm outside Utilita Arena in a drive-by attack
He was taken to hospital with serious but not life-threatening injuries.
Anyone with information is urged to call West Midlands on 101, or those with photos or video footage which could help the investigation can visit the force's dedicated web page.
Alternatively, call Crimestoppers anonymously on 0800 555111.