Saudi Arabia has not, at this stage, worked out who is behind the attacks, but the Huthirbells have previously taken similar actions.
One of the attacks occurred at an oil plant in Buqyag, which is near the city of Dammam in the eastern province of the kingdom. Videos from the site show fire and smoke, according to the news agency.
The second attack must have occurred on the Khurais oil field.
According to a local news channel, the plants are owned by Saudi Aramco - the world's largest oil company, according to AP.