The exact circumstances of the incident at the remote guard post were not immediately clear, although there was no indication that North Korea was involved in the incident.
The incident took place in the Goseong county, a mountainous region that borders the North on the eastern end of the peninsula.
A separate official with the army said there was an operation to capture the conscript who is believed to be on the run carrying a firearm, live ammunitions and a grenade.
All able-bodied South Korean men must serve about two years under a conscription system that makes up a military of more than 600,000 troops aimed at deterring aggression by North Korea, which is one of the world's most militarised states.
Incidents involving firearms at South Korean military units are not frequent but have occurred in the past, typically when conscripts who had been under stress opened fire on other unit members or deserted the base carrying weapons.
The tensely guarded border across the Korean peninsula was drawn up at the end of the 1950-53 Korean War. The two Koreas remain technically at war because an armistice and not a peace treaty was signed to end the conflict.
North Korea stations a large portion of its 1.2-million strong military near the border backed by artillery power. It regularly threatens the South and the U.S. military based in the South with destruction.
Earlier on Saturday, the North's official KCNA news agency accused the South's president and its defence chief as "criminals" who fueled military tension in commentary typical of rhetoric from Pyongyang that warned of war.
