The altercation happened on Tuesday in a small town near Ulricehamn. A knife-wielding man had attacked a woman, prompting a police patrol to shoot him in the stomach at around 7pm.
"When we arrived on the scene we saw through the window that the man was attacking the woman with a knife. Officers tried to put a stop to the attack using batons, among other things, but didn't succeed," Henrik Sterner of the Västra Götaland police told the TT news agency.
Police confirmed on Wednesday morning that the man had died in hospital.
He had stabbed the woman multiple times, including in the head and back.
The woman remains in hospital in a critical condition, but her injuries are not considered to be life-threatening.