The fatalities were a Saudi citizen and a Yemeni resident, the Saudi Press Agency and other media reported.
Lt Col Mohammed Al Hammad, spokesman for the General Directorate of Civil Defence, said a projectile had been launched by Iran-backed Houthi rebels from inside Yemeni territory towards Samtah governorate in Jazan region.
Civil defence teams sent to the site discovered “a military projectile” had fallen on a shop on the main street, resulting in the two deaths.
Six of the wounded were Saudi civilians and one was a Bangladeshi resident, SPA reported.
Earlier on Friday, the Saudi-led coalition has said it had destroyed nine Houthi weapons depots near the Yemeni capital Sanaa.
A military operation targeted the Tashreefat military camp run by Iran-backed Houthi rebels, the Saudi state news agency quoted the coalition as saying.
The Houthis have launched repeated cross-border drone and missile attacks on Saudi Arabia since the Saudi-led coalition intervened in Yemen in March 2015, after the rebels ousted the internationally recognised government from Sanaa.