The projectile also left six Saudis and one Bengali resident injured and it damaged 12 cars and two shops, the Saudi state news agency said.
The Saudi-led coalition fighting the Iran-aligned Houthis in Yemen carried out an attack later on Friday in response to what it called "the attack's origins" and said it will follow that with a wider attack on Houthi military targets.
Houthi military spokesman Yahya Sarea wrote on Twitter on Saturday that three ballistic missiles targeted "critical" sites in Jazan.
The main Houthi news outlet Al Masirah TV said a child and a woman were killed and seven more were injured in coalition strikes on Yemen's Al Mahwit governorate.
Another Houthi Projectile hit Saudi's Najran city causing material damage.
Coalition forces struck a Houthi military camp in the centre of the Yemeni Capital Sanaa early on Friday, with residents telling Reuters explosions rocked the city.
The coalition intervened in Yemen in 2015 after the Houthis ousted the internationally recognised government from Sanaa.