Video obtained by Reuters showed the fire engulfing multiple sections of the site in Abqaiq.
The videographer, who declined to be identified, told Reuters he was woken up by the noise coming from the refinery.
Abqaiq, about 37 miles southwest of Dhahran in Saudi Arabia's Eastern Province, contains the world's largest oil processing plant. Most Saudi oil exported from the Gulf is processed there.
The precise targets and the extent of possible damage were unclear. Aramco did not immediately respond to a request for comment.
Tensions are running high in the region after attacks in June and July on oil tankers in Gulf waters that Riyadh and Washington blamed on Iran. Tehran denies the accusations.