Police were first called to the scene shortly after 7pm when they received of a report that an armed man had been spotted in central Bagarmossen, a south-eastern suburb of Stockholm.
“The man departed in a car which was seen by a police unit and stopped on Sockenvägen,” Mikael Pettersson at Stockholm Police told news agency TT.
“The driver got out and shot at the police unit, who returned fire.”
Newspaper Aftonbladet reported the man had been shot in the head.
Pettersson said he did not know how many shots had been fired in the exchange but noted there were four bullet holes in the police car’s windscreen.
The shooting victim, born in 1988, was taken by air ambulance to Karolinska University Hospital in Solna where doctors were unable to resuscitate him.
The man was the tenth person to be shot dead by Swedish police since January 2013.
The victims of police shootings include a sword-wielding right-wing extremist who killed three people in an attack on a school in Trollhättan in western Sweden last year.
In May 2013 police shot and killed a 69-year-old man in Husby outside Stockholm. That shooting was widely cited as the spark for a wave of riots and vandalism in the area. The victim's widow described it as an “execution”. Prosecutors later vindicated the police, saying they had acted in self-defence.