Police say the man had been attacking the woman with a knife, and after trying other means to stop him, they shot the man in his abdomen.
The prosecutor who looked into the shooting said that the woman's life was in danger.
"My understanding is that the police aimed as low as he could, without risking that the bullet would hit the woman. The circumstances were such that it was not obviously indefensible to shoot. That the man later died does not change that judgement," says Lena Lithner, the chief prosecutor on the case, to news agency TT.