Severe Tropical Cyclone Ilsa crossed the coast near Port Hedland just before midnight (17:00 BST) on Thursday as a category five storm.
It has since been downgraded to category four but still has the potential to cause significant damage.
A red alert was issued hours earlier, with thousands of people ordered to take immediate shelter.
It is the country's most serious cyclone alert level. Under it, people are told to remain in the strongest, safest part of their homes and to stay away from doors and windows until they are given the all clear by authorities.