A large plume of smoke and fire was seen rising in the vicinity of an Aramco facility in Riyadh on Saturday, a witness told Reuters.
There was no immediate confirmation from Saudi authorities about the fire.
Later on Saturday, the Houthis claimed the attack and said they targeted the Aramco facility with ballistic missiles and drones.
There was no immediate confirmation from Saudi Arabia.
The fire comes amid escalating hostilities between Saudi Arabia and Yemen's Iran-aligned Houthis, who have stepped up attacks on Saudi cities and energy infrastructure.
There was no immediate claim of responsibility for Saturday's fire.
Facilities reportedly hit in Saudi Arabia, many targets struck in Yemen
The Houthis said last week they had attacked Saudi Aramco facilities in Yanbu with missiles and drones. Saudi Arabia said at the time that it had intercepted six ballistic missiles fired by the Houthis towards Taif and the Yanbu area, but did not report damage to Aramco facilities.
Later, Yemen's Houthi-run Al Masirah TV reported early on Sunday an attack carried out by Saudi Arabia on Yemen's capital of Sanaa. Saudi Arabia has not yet confirmed that it carried out the strike.
Houthi military spokesman Yahya Sarie claimed earlier that 94 airstrikes were carried out in Yemen on October 1.
The attacks were allegedly carried out using fighter jets and missiles and targeted civilian sites in the provinces of Sana'a, Saada, Taiz, Hajjah, Amran, and Al Bayda.