Houthi supporters have been staging rallies against the Saudi-led air raids
It was intercepted by a Patriot missile battery near the south-western city of Khamis Mushait in the morning.
On Friday, four Saudi soldiers and many Yemeni rebels died in fighting on the border, the Saudi-led coalition says.
It says forces loyal to Yemen?s former president, backed by the Houthis, attacked several Saudi positions.
In a separate development, the Houthis have agreed to attend peace talks in Geneva.
The UN-brokered meeting on 14 June in Switzerland is aimed at ending weeks of war that has claimed more than 2,000 lives.
?We accepted the invitation of the United Nations to go to the negotiating table in Geneva without preconditions,? Daifallah al-Shami, a senior member of the rebels? political wing told AFP.
Yemen?s government, which is operating from Riyadh, also said it would attend.
A Saudi-led coalition has been bombing rebel positions in Yemen for 10 weeks, in support of the country?s exiled president Abdrabbuh Mansour Hadi.
The Houthis overran the capital Sanaa last September and have gone on to seize most of the country.
Although there have been previous border skirmishes and deadly rebel fire against Saudi Arabia, Friday?s battle is only the second major ground attack reported against Saudi territory.
The rebels ?aimed to penetrate our borders?, and were eventually repelled, the Saudi statement added.
The humanitarian crisis in Yemen has been described as ?catastrophic? by the UN with 20 million civilians ? 80% of the population ? in need of aid.
At least 21 people have died during violence since Thursday in the Aden area, while there were intense coalition air raids against Daleh and Shabwa provinces.