The man who died - who was thought to be in his 40s - was chased through the square in the centre of Rinkeby before being stabbed and then shot just after 2pm on Sunday afternoon.
A witness told Swedish newspaper, Aftonbladet, that he was sitting on a bench outside Lidl when he saw two men chasing one of the victims. "One of the men ran after the guy with a gun, the other with a knife," said the witness.
“The guy was stabbed first and then shot right here in the square,” he continued.
Another witness who was nearby stated: “I heard four or five shots and decided to run away. There were several others who also started running and I saw one of them was injured in the leg”.
“We regard it as an extraordinary event,” said Eva Nilsson of Stockholm police.
“If we have to use the whole county's resources we will,” Nilsson added.
The other injured victims are thought to have been hit by ricochets.
At 5pm on Sunday afternoon, three men surrendered to the police in western Stockholm and were arrested.
While Malmö in southern Sweden has been rocked by a summer of violence with several shootings and explosions in recent months, Stockholm has remained comparatively calm.
But five weeks ago a 19-year-old died in hospital after he was found with gunshot wounds between the Rinkeby and Bromsten areas north of Stockholm. That incident has not been linked to the murder this afternoon.
Rinkeby, a district of Västerort in Stockholm, was one of several areas which saw violent unrest in 2013, with up to 30 fires a night and several police injured by stones.