The western territory is a tinderbox of ethnic and religious divisions and security forces have clashed with both Rohingya insurgents and much better armed Rakhine fighters from the mostly Buddhist Arakan Army.
Private Aung Kyaw Thet went missing in action after an ambush last week by unknown assailants in Maungdaw township near the border with Bangladesh.
His body was found two days ago with "gunshot wounds in his face, arm and leg near a hill inside the other country," according to government-backed Global New Light of Myanmar.
The ambush happened the same day that two ethnic Rakhine Buddhist men disappeared while fishing in the same township and were later found with their throats slit, prompting the army to launch local "clearance operations" and raising fears of renewed large-scale violence.
Sunday's report in Global New Light did not identify the alleged perpetrators of the shooting but said authorities found foxholes near the scene, bullet casings and biscuits manufactured in Bangladesh.
More than 720,000 Rohingya fled northern Rakhine to Bangladesh after Myanmar launched a crackdown on the Muslim minority in August 2017.
UN investigators want senior Myanmar generals to be prosecuted for genocide but the army says it was responding to attacks on border guard posts by Rohingya insurgents that killed around a dozen security forces.
The army this week called a rare ceasefire against ethnic armed groups in the northeast of the country but Rakhine state was not included.
Analysts say the military left Rakhine out because it does not want the Arakan Army to gain a foothold in the state as well as lingering concern over the less powerful Rohingya militants, who call themselves the Arakan Rohingya Salvation Army.