The Arabic-language Sabq News news website, citing unnamed security sources, reported on Monday that the soldier, whose identity was not immediately known, opened fire on fellow soldiers at a base in the Abu Arish district of the region, located 966 kilometers south of the capital Riyadh, Presstv Reported.
The sources added that a personal conflict between the shooter and a staff sergeant had motivated him to kill his comrades.
The soldier turned himself in to security officials and handed over his assault rifle after the incident.
Jizan region police have yet to release an official statement about the shooting, and the circumstances surrounding it.
On April 21, four assailants targeted state security forces in Zulfi City, located about 260 kilometers north of Riyadh.
The London-based Arabic-language daily newspaper Asharq al-Awsat reported that they had rammed a vehicle into a security barrier around the station in an attempt to gain entry.
Two gunmen then stepped out of the vehicle and opened fire, sparking a gun battle with police.
A third attacker attempted to flee but was also gunned down, while a fourth died as he tried to set off an explosive belt.
There were no immediate reports about casualties among the security personnel.
Militants have targeted security installations in Saudi Arabia for years.
Back in early April, two assailants were killed and two others got arrested in an attack on a security checkpoint in the oil-rich and Shia-populated Eastern Province.
Al-Arabiya television news network said the incident had occurred on Abu Haidriyah Highway, which links Bahrain to Saudi Arabia and extends to the Kuwaiti border. The assailants were reportedly attempting to evade the security checkpoint as they sought to flee the country.