Swedish prosecutors say they arrested three Free Aceh Movement (GAM) leaders "suspected of grave breaches of international law" on Tuesday.
Two are being held in custody. Indonesia identified them as GAM chief Hasan di Tiro, the self-styled Aceh foreign minister Zaini Abd Allah and its "prime minister" Malik Mahmud.
Three Indonesian officers have already left Jakarta and will seek permission to question the three, said national police spokesman Paiman.
Indonesian officials have welcomed the arrests and called on guerrillas in the field to surrender.
However, local Swedish media suggest the three suspects may soon be released as much of the documentation seized in connection with the arrests has not been translated accurately.
The Swedish broadsheet, Dagens Nyheter, said unless some proof that the suspects are linked to any violent separatist activities, all three would have their charges dropped.
An estimated 10,000-12,000 people, many of them civilians, have been killed in the independence war which GAM launched in 1976.
Most died during an army offensive between 1989 and 1998, which was marked by gross rights violations by the Indonesian military.
Jakarta has been pressing Stockholm for the past year to curb the activities of GAM's exiled leaders.
Swedish prosecutors visited Aceh in March to assess whether the exiles, most of whom have Swedish passports, were directing violence on the ground.
The military launched a major offensive against GAM just over a year ago after an internationally mediated truce broke down.