The dead officer was shot in the chest and abdomen. Another police officer who was taken to hospital after being shot in the arm was said by Nyköping Hospital to have sustained only minor injuries.
A man has been arrested on suspicion of shooting the pair.
The officers were shot at 5:20pm in the centre of the town. They were taken to hospital, and at 6pm there was no word on how serious their injuries were.
A cordon was placed around a building in central Nyköping, local paper Södermanlands Nyheter reported.
No motive for the shooting has so far been identified. A woman who lives near the scene told news agency TT:
“I was washing up and thought I heard someone shooting. When I went to the window I saw how a man was shooting at a woman who was sheltering behind a car.”