Some Papuans have an uneasy relationship with the government in Jakarta
The soldiers are accused of luring their victims to a meeting with the promise of selling them weapons.
According to police, the soldiers killed them and then dismembered their bodies before stuffing them into sacks and throwing them into a river.
Indonesia has a heavy military presence in the Papua region, where separatist groups are waging an insurgency.
Papua, a former Dutch colony, declared independence in 1961, but Indonesia took control of the eastern region two years later.
Police and military authorities said they were conducting a joint investigation into the killings, which are said to have taken place on 22 August near the city of Timika.
They said investigators were questioning the suspects, whose names have not been released.
Papua provincial police director Faizal Ramadhani told the AFP news agency that body parts belonging to three of the victims had been found.
He added that authorities were continuing to look for the remains of the last victim.
The West Papua National Liberation Army, the military wing of Papua's main separatist group, described the killings as "a crime against humanity by the Indonesian government through its security forces".
The group called on the Indonesian government to sentence the perpetrators to death, saying that it would carry out a "retaliation operation" if its demand was ignored.
-- Courtesy of BBC News