There was no immediate Saudi comment on the report.
"The air force announced the execution of air strikes with the Qasif 1 aircraft on Aramco in Jizan (province)", al-Masirah said on its official Twitter account, according to Reuters.
Yemen's Houthi rebels later claimed responsibility for the incident saying they had targeted Saudi Arabia's defence ministry in Riyadh with ballistic missiles.
The missile is thought to have been fired by Houthi rebels in Yemen, who a Saudi-led coalition has been bombing since March 2015, when it intervened in support of ousted President Abdrabbuh Mansour Hadi in an effort to prevent Houthis from maintaining the capital of Sanaa.
"The missile force carried out a large-scale ballistic missile attack on various parts of Saudi Arabia", the group's Al-Masirah TV said.
The coalition has launched thousands of air strikes in Yemen which have hit schools, markets and hospitals, killing hundreds of people - though it says it does not target civilians.
The missile was shot down just hours after Saudi military brought down a Houthi-rebel drone at an worldwide airport in the southern city of Abha. Iran denies arming the rebels.
"The air force announced the execution of air strikes with the Qasef-1 aircraft on Aramco in Jizan (province)", the channel said on its Twitter account, referring to a drone the Houthis unveiled a year ago.
As the announcement on the missile interceptions emerged, Malki also said in a separate statement that Saudi air defences had shot down two unmanned Yemeni drones in southern Saudi Arabia.
Drones operated by Yemeni armed forces have targeted a Saudi airport and a facility belonging to the state-run oil giant Aramco in the kingdom's southern border regions.
Yemen lies along one of the main global oil chokepoints in the Red Sea.
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