Police arrested the trio, aged between 22 and 29, on Sunday morning.
"It has not yet been established what role the people played in this; they haven't been interviewed as yet," said Kjell Lindgren at Stockholm police to the TT news agency.
"We will try to establish If there was one person or more people doing the shooting in the course of the investigation," Lindgren said.
The police were unwilling to comment on the conditions surrounding the arrests.
Two of the victims are reported to be in a serious condition and remain in hospital under police surveillance.
"We are there for three reasons. They have been targeted in a serious crime and we want to interview them as soon as possible. We also want to be there if something happens at the hospital. And we are there as security for the staff at the hospital."
The shootings were called in to the police shortly before 9pm on Saturday evening. A witness told the Expressen daily that there were some 25-30 people at the restaurant at the time.
"There were two guys sitting at the bar drinking beer. Then a guy came in and shot them. There was panic. People starting to shout and hide," the witness told the newspaper.
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A massive police operation was launched and the manhunt continued though the night. The men are believed to have fled in a grey Saab.
The two men were taken directly to hospital while a third checked himself in later with gunshot wounds to the leg.
All three injured men are in their thirties and known to the police.