According to the company, the Gorgon and Wheatstone facilities in Australia account for more than five percent of the world's liquefied natural gas.
Work is underway to restore production at the facilities, which were hit by a power outage on Thursday afternoon.
A third facility in Australia, belonging to the energy company Woodside, has also suffered production interruptions related to the cyclone.
The events are taking place at a time when the world is focusing heavily on oil and gas due to the Iran war's impact on supply.
Cyclone Narelle is still moving along the coast of Western Australia.
