"Witnesses saw a man running from the scene of the crime," Ulla Brehm of Västra Götaland police told the Expressen newspaper.
The woman was shot in a car park in Högsbohöjd, an area in Gothenburg in western Sweden, at around 7am. Police officers were on the scene soon after, together with sniffer dogs, helicopters and paramedics.
The woman was taken to hospital where she later in the morning died from her injuries.
It remains unknown if there are any witnesses to the shooting.
"I couldn't say if someone saw it. We have differing information but we've gotten a lot of help from local residents and people who were in the area. We're putting together the puzzle pieces," Brehm said.
The police have cordoned off the area and are searching for anyone with more information. A forensic investigation has been launched.