The Saudi-led military coalition fighting the Iran-aligned Houthi rebels said a missile launched by the militia had been intercepted and destroyed.
Saudi Aramco is one of the most valuable companies in the world.
It is headquartered in the Dammam metropolitan area in eastern Saudi Arabia, from where oil production and exports are managed.
The Houthis earlier threatened to attack Aramco's headquarters and launch further strikes on Riyadh airport if Saudi Arabia attacked the Yemeni capital Sanaa, which the Houthis have controlled for about a decade.
Houthi military spokesman Yahya Saree said the movement had attacked the Aramco HQ and other targets using drones, missiles and cruise missiles, causing "fires and destruction".
Further attacks on Saudi airports and energy facilities would follow, he said.
Saudi civil defence authorities reported that two cruise missiles had been intercepted over Riyadh during the night.
Falling debris injured four people and damaged 15 houses.
Meanwhile, fighting continued in Yemen, including in the province of Taiz, where clashes have been raging for weeks.
Sources within government forces said the Houthi rebels had seized a key access point to the city of Taiz after heavy clashes with soldiers from the internationally recognised government.
Taiz is Yemen's third-largest city and was besieged for years during the civil war.
Houthi fighters are seeking to take complete control of this strategically important city.
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