The five were arrested in connection with the incident and ordered detained by a prosecutor, Swedish police said on their website. They did not say if the shooter was among those detained.
Salwan Momika, 38, was shot in a house in the town of Sodertalje near Stockholm, public broadcaster SVT reported, citing unnamed police sources.
Momika had burned copies of the Koran, the Muslim holy book, in public demonstrations in 2023 against Islam.
Police attend the scene of the shooting in Sodertalje south of Stockholm. (EPA PHOTO)
A Stockholm court had been due to sentence Momika and another man on Thursday in a criminal trial over "offences of agitation against an ethnic or national group," but said the announcement of the verdict had been postponed.
A police spokesperson confirmed a man was shot dead in Sodertalje, but gave no other details.
The other defendant in the same court case was giving interviews on Thursday and posted a message on X, saying: "I'm next".
The Security Service said police were leading the investigation but "we are following the development of events closely to see what impact this may have on Swedish security," a spokesperson told Reuters.
Swedish media reported that Momika was streaming live on TikTok at the time he was shot. A video seen by Reuters showed police picking up a phone and ending a livestream that appeared to be from Momika's TikTok account.
Sweden in 2023 raised its terrorism alert to the second-highest level and warned of threats against Swedes at home and abroad after the Koran burnings, many of them by Momika, outraged Muslims and triggered threats from jihadists.
While the Swedish government condemned the wave of Koran burnings in 2023, it was initially regarded as a protected form of free speech.
Sweden's migration agency in 2023 wanted to deport Momika for giving false information on his residency application, but couldn't as he risked torture and inhumane treatment in Iraq.
Burning the Koran is seen by Muslims as a blasphemous act because they consider it the literal word of God.
