Two civilians were killed in a shelling, carried out on Saturday by Yemen's Houthi militants on the Saudi southwestern city of Jazan, the Saudi Al-Ekhbariya TV channel reported citing Saudi-led Arab coalition's statement.
The UN and aid agencies have pleaded with the Saudi-led force against an attack on Hodeida, warning that it could lead to mass civilian casualties and starvation.
"The Arab coalition will strike with an iron fist all those who threaten the safety and security of Saudi nationals, residents and capabilities".
On Tuesday, Riyadh's air defence systems intercepted a Houthi missile fired from Yemen at the Saudi city of Yanbu, north of Mecca and Jeddah.
It came as coalition-backed Yemeni forces advance on the rebel-held Red Sea port of Hodeida, the main conduit for humanitarian supplies into a country teetering on the brink of starvation.
The latest strike at Saudi Arabia comes as Yemeni forces, backed by the coalition, advance on the rebel-held Red Sea port of Hodeidah, the main conduit for humanitarian supplies into a country on the brink of starvation.
Saudi Arabia launched a war against the Houthis in March 2015, after the rebels drove Yemen's internationally recognised government from the capital, Sanaa.
The three-year conflict has killed more than 10,000 people and displaced more than 3 million.