Emergency services found the man in a stairwell in Majorna on Monday evening.
"He died later from his injuries. People heard shooting in the area and we found bullet casings in the stairwell's entrance," Peter Adlersson of the local police told the TT news agency.
Two people, a man and a woman, were arrested late on Monday morning. It remains unclear what relation they have to the deceased man.
Police have labelled the crime as murder, with the alternative of manslaughter, and have launched a forensic investigation.
Officers added that they do not see any connection to other shootings that have taken place in Gothenburg recently.