A border post was attacked overnight by Huthi rebels, a spokesperson said, adding that one soldier wounded in the exchange died before reaching hospital.
He was the latest of at least 111 Saudi soldiers and civilians to die in the country's south since the kingdom launched a coalition to battle Yemeni insurgents in March 2015.
Most Saudi casualties have been from retaliatory cross-border rocket attacks or combat.
Mine kills Saudi soldier near Yemen border
But there have also been previous deadly mine blasts in Jazan.
In Yemen itself, more than 7,000 people have been killed, mostly civilians, since March last year according to the United Nations.
A Yemeni military official said Sunday that five rebels were killed in a coalition air raid in the southern Shabwa province.
Also in Shabwa, three armed tribesman were killed in an ambush by fighters belonging to the Yemeni branch of Al-Qaeda.
Yemen's conflict has allowed militant groups including Al-Qaeda and the Islamic State group to expand, mainly in the country's vast desert east.
Landmine kills Saudi soldier on Yemen border
President Abedrabbo Mansour Hadi Sunday visited the port city of Mukhalla, on Yemen's southeast coast, for the first time since loyalist forces retook it from militants.
In Shibam, around 100 kilometres (65 miles) north of Mukhalla, a local official survived an assassination attempt blamed by security sources on Al-Qaeda.
The sources said Faraj Neji survived the ambush but that two of his guards were killed.
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