The 12-year-old had been arrested for alleged involvement in a crime case, an accusation his family denies.
The boy, who was a memorizer of the Quran, was killed while in custody and the military returned his body to his family without giving any explanation, according to Arakan news agency.
The family are among a few remaining in Nurula village near Maungdaw, a town in Rakhine State, in the western part of Myanmar.
Most of the residents have fled to Bangladesh following a massive crackdown by the army against Rohingya Muslims.
More than 630,000 have arrived in Bangladesh since August when the crackdown began on members of the community.
Many villages and towns populated by the Muslims were torched and looted after suspected Rohingya militants attacked police and border posts in Rakhine.