Online videos apparently shot in Buqyaq included the sound of gunfire in the background. Smoke rose over the skyline and glowing flames could be seen a distance away at the Abqaiq oil processing facility.
The fires began after the sites were "targeted by drones", the Interior Ministry said in a statement carried by the state-run Saudi Press Agency. It said an investigation into the attack was underway.
Saudi Aramco, the state-owned oil giant, did not immediately respond to questions. The kingdom hopes soon to offer a sliver of the company in an initial public offering.
The company describes its Abqaiq oil processing facility in Buqyaq as "the largest crude oil stabilisation plant in the world."
The facility processes sour crude oil into sweet crude, then later transports onto transshipment points on the Persian Gulf and the Red Sea. Estimates suggest it can process up to 7 million barrels of crude oil a day.
The plant has been targeted in the past by militants. Al-Qaeda-claimed suicide bombers tried but failed to attack the oil complex in February 2006.
The Khurais oil field is believed to produce over 1 million barrels of crude oil a day. It has estimated reserves of over 20 billion barrels of oil, according to Aramco.
There was no immediate impact on global oil prices as markets were closed for the weekend across the world. Benchmark Brent crude had been trading at just above $US60 ($87) a barrel.
Buqyaq is some 330 kilometres north-east of the Saudi capital, Riyadh.
Suspicion immediately fell on Yemen's Houthi rebels. A Saudi-led coalition has been battling the rebels since March 2015. The Iranian-backed Houthis hold Yemen's capital, Sanaa, and other territory in the Arab world's poorest country.
The war has become the world's worst humanitarian crisis. The violence has pushed Yemen to the brink of famine and killed more than 90,000 people since 2015, according to the US-based Armed Conflict Location & Event Data Project, or ACLED, which tracks the conflict.
Since the start of the Saudi-led war, Houthi rebels have been using drones in combat. The first appeared to be off-the-shelf, hobby-kit-style drones. Later, versions nearly identical to Iranian models turned up. Iran denies supplying the Houthis with weapons, although the UN, the West and Gulf Arab nations say Tehran does.
The rebels have flown drones into the radar arrays of Saudi Arabia's Patriot missile batteries, according to Conflict Armament Research, disabling them and allowing the Houthis to fire ballistic missiles into the kingdom unchallenged. The Houthis launched drone attacks targeting Saudi Arabia's crucial East-West Pipeline in May as tensions heightened between Iran and the US. In August, Houthi drones struck Saudi Arabia's Shaybah oil field, which produces some 1 million barrels of crude oil a day near its border with the United Arab Emirates.
UN investigators said the Houthis' new UAV-X drone, found in recent months during the Saudi-led coalition's war in Yemen, likely has a range of up to 1500 kilometres.
That puts the far reaches of both Saudi Arabia and the UAE in range.
The Houthi's Al-Masirah satellite news channel did not immediately acknowledge the attack on Saturday.
AP