A police spokeswoman says that several witnesses have come forward, after they heard shots fired in the Högsbohöjd district just after 7 AM.
When police arrived on the scene they found the woman, seriously injured in the arm and the face. She died before she could be taken to hospital.
The area is now sealed off, and police are using dogs and a helicopter to search it, plus door-to-door talking to witnesses.
Prosecutor Anette Ohlsson says that in this case a restraining order may not have done any good, since those who want to hurt someone may not be prevented by a legal ban."