The Jakarta Globe reported that Ja'far Umar Thalib is the former commander of the disbanded Islamist militant organisation Laskar Jihad.
Ja'far, a leading proponent of a puritanical form of Islam with a long history of involvement in sectarian conflict, runs an Islamic boarding school in Keerom district.
Police alleged Ja'far incited his followers to attack the house of a resident in Jayapura, 30 kilometers to the north.
The resident was reportedly confronted at around 5.30am by several sword-wielding people dressed in white.
The pretext for the alleged attack was that he played music too loud and that it disrupted morning prayers at a nearby mosque.
The local chapter of Indonesia's top Muslim clerical body, the Indonesian Ulema Council, previously warned that Ja'far and his followers could disrupt delicate religious harmony in Papua.