"Saudi Aramco's response team controlled a limited fire this morning at the Shaybah natural gas liquefaction facility," the energy giant said. "There were no injuries and no interruptions to Saudi Aramco's oil operations."
The Houthi rebels have carried out a spate of cross-border missile and drone attacks targeting Saudi air bases and other facilities in recent months in what it says is retaliation for the Saudi-led air war in Yemen.
Early on Saturday the Houthis issued a statement claiming a "massive" attack against a Saudi gas installation, which they said was hit by 10 drones.
A rebel spokesman, cited by the insurgent television station al-Masirah, also vowed "fiercer and larger attacks" against Saudi Arabia should it retaliate.
Saudi Energy Minister Khalid al-Falih said the latest attack was carried out at 3.20am GMT by "booby-trapped drones".
Saudi Arabia "staunchly condemns" the attack, he said.
"This terrorist sabotage follows a series of actions, including attacks against oil tankers, are aimed at disrupting international oil supplies," Falih said.
"These acts are not only aimed at Saudi Arabia but also against the global economy," he added.
Tensions in the Gulf have soared since May, with US President Donald Trump calling off air strikes against Iran at the last minute in June after the Islamic republic downed a US drone.
The United States and Saudi Arabia have also blamed Iran for multiple attacks on tankers in the Gulf.