A huge fire began after the Saudi Aramco sites were targeted by drones, the ministry said in a statement carried by the state-run Saudi Press Agency.
It was not clear if there were any injuries in the assault on the processing plant in Buqyaq and at the Khurais oil field.
The fires are now under control at both facilities, it said.
No one immediately claimed responsibility for the attacks. The ministry said investigations were going on.
The plant has been targeted in the past by militants.
Saudi Aramco describes its Abqaiq oil processing facility in Buqyaq, 330 kilometres north-east of the Saudi capital, Riyadh, as the largest crude oil stabilization plant in the world.
