The 35-year-old woman, who is reported to have three children, was found lying outside of a residential building in the Sävedalen area of the city.
“First we thought that it was an accident, but then it emerged that she had been shot,” said police spokesperson Thomas Fuxborg.
The woman was rushed to Östra hospital after police responded to an alarm call at around 6.30pm, where she remains with her life in the balance.
Police spent Saturday evening talking to the woman’s neighbours, the local Göteborgs-Posten daily reported.
“They asked if we had seen anything special but did not tell us what had happened,” said one neighbour to the newspaper.
By 11am on Sunday the police had not established a suspect in the shooting, while it was confirmed that the woman’s condition remained life-threatening.
Police were neither willing to confirm whether the woman was shot at the scene or whether she had been left there.