Yemen's Houthis say missile attacks on the kingdom are in retaliation for air raids on Yemen by the Western-backed coalition.
The facility reportedly belonged to the oil giant Saudi Aramco.
The attacks mark the fourth time in five months that missiles have flown over Riyadh, as the Houthis step up efforts to demonstrate they can reach the Saudi capital.
Wednesday's missiles followed the downing of two Houthi drones earlier in the day in Jizan and the nearby Saudi city of Abha, the coalition said.
The channel did not provide any details on casualties of damage from the alleged attack, however Saudi authorities said its facilities in Jizan were operating "normally and safely" following the Houthis' announcement.
One of the drones was targeting the Abha worldwide airport in Asir province, which led to a temporary suspension of air traffic.
More than 10,000 Yemenis have died in the conflict and millions in the impoverished country have been pushed to the brink of starvation.
Wednesday's attacks were claimed by the rebels via their news outlet Al-Masirah.
Saudi Arabia accuses its rival Iran of smuggling missiles to the Huthis - a charge Tehran denies.
"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. The group unveiled the Qasef-1 drone previous year.
Meanwhile, the Yemeni Defense Ministry reported that 30 Houthi fighters were killed in the air bombardment by Saudi-led warplanes in central al-Bayda Province.
More recently, the Houthi movement claimed to have fired a ballistic missile targeting Saudi Aramco in the southern Saudi province of Najran three weeks ago.
Yemen lies along one of the main global oil chokepoints in the Red Sea.
Batrawy reported from Dubai, United Arab Emirates.