A boy was killed and around eleven people injured in the shootings in the Tolikara centre of Karubaga, amid unrest in which shops and a small mosque were burnt.
Religious leaders signed a peace treaty following the incident a month ago.
The Jakarta Post reports Papua's police chief Paulus Waterpauw has said closure resulting from the treaty would not last long as it would not be accepted by certain groups.
He says the incident must be legally processed and not just dealt with by customary settlement.
Two people have so far been charged for allegedly inciting a riot which saw a mosque burnt and fears triggered of sectarian violence across Indonesia.