Gang leader Mustafa "Benzema" Aljiburi was shot dead in a car in Iraq on Monday.
A Swedish man in his twenties is suspected of the murder and has been apprehended, according to reports.
Two other Swedes have also been arrested.
The police are working on the theory that several people may have collaborated in the shooting.
The assumption is that a companion drove a car behind the motorcycle-mounted shooter, filming the act.
The information about Aljiburi's death has also reached the Swedish police and the Ministry of Foreign Affairs.
The Swedish man arrested in connection with the murder has previously been convicted of serious firearms offences and several drug offences.
He also appeared in a murder investigation in Gävleborg, where a young man was shot dead.
This murder is linked to local criminal groups.
Two more Swedish citizens have been arrested on suspicion of the murder, according to Svenska Dagbladet, citing police sources.