The shooting occurred in al-Mashnaq border on Sundaynight, a website related to the Houthi group reported.
Hassan Ajibi was killed in the incident and Mohamed Hazem al-Zahvi was seriously wounded when he was trying to cross the border.
Saudi border guards took the dead body of Ajibi.
Houthi Shia fighters say Saudi Arabia gives military equipment and weapons to the Salafi forces in northern Yemen to fight the Houthis.
