The Saudi statement came just hours after the Yemeni group claimed to have launched the attack.
State-owned TV channel Al Ekhbariya reported on Friday that Saudi defence forces intercepted the missile over Najran, a region straddling the kingdom’s southern border with Yemen, before it could hit its intended target.
Al Masirah, a TV network run by the Houthi rebels, said the group claimed responsibility for the attack via Twitter, saying it had a “successful launch of a short range ballistic missile at a military target in Saudi Arabia”.
It said the the rebels fired a Qaher-2M missile of Soviet origin towards a military installation in Najran. The missile has a range of up to 400km.
Al Masirah also said that within hours of the missile attack, the Saudi coalition bombing Yemen retaliated with several air raids on Saada, an impoverished Houthi stronghold.
Al Jazeera could not independently verify the network’s claims.
Saudi Arabia, supported by the US and other countries, have launched more than 15,000 air attacks against Houthi targets since March 2015, while dozens of missiles have been fired into the kingdom from Yemen.
Last month, the Houthis said that one of their missiles hit a military target inside Saudi Arabia, without specifying the location.
Saudi officials, however, said they intercepted the missile.
The Saudi-led coalition has previously accused Iran of helping arm the Houthis, accusing Iran of “flagrant military aggression” and “manufacturing and smuggling [missiles] to the Houthi militias in Yemen for the purpose of attacking the Kingdom, its people, and vital interests”.
Iran has repeatedly rejected allegations of arming the Houthis, calling them “malicious, irresponsible, destructive and provocative”.
The war in Yemen, the region’s poorest country, started in 2014 after Houthi rebels seized control of the capital Sanaa and began pushing south towards the country’s third-biggest city, Aden.
Concerned by the rise of the Houthi rebels, believed to be backed by Saudi Arabia’s regional rival Iran, the kingdom and a coalition of Sunni Arab states launched an intervention in 2015 in the form of a massive air campaign aimed at reinstalling President Abd-Rabbu Mansour Hadi’s government.
Since then, more than 10,000 people have been killed and at least 40,000 wounded, mostly from Saudi-led air attacks.