The shooter was slightly wounded and has been taken into custody, officials said. The motive for the shooting remains unclear.
The island base is near a disputed maritime border with North Korea.
All able-bodied South Korean men are required to serve at least two years in the country's 650,000-member military.
In Monday's incident, a staff sergeant, a corporal and a lance corporal were killed, while a corporal and a private were injured, Yonhap news agency quoted an unidentified military official as saying.
It is unclear whether the perpetrator hurt himself or was injured while being apprehended.
The incident was being investigated, defence officials said.
There have been previous violent incidents involving South Korean soldiers in recent years.
In 2005, a young soldier threw a grenade and fired at sleeping comrades, killing eight and seriously injuring two.
In 2008, a private reportedly injured five other soldiers when he threw a grenade at them while they were sleeping.
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