The category three system is expected to bring massive storm surges of up to five metres, flooding and destructive winds of about 200 kilometres an hour.
Tropical Cyclone Warning Centre forecaster Greg Browning says the cyclone made landfall north of Whim Creek overnight.
"Around the eye of the cyclone we could see gusts of up to 220 kilometres per hour," he said.
A red alert has been issued for residents in Port Hedland, Karratha and communities between Pardoo and Mardie.
Port Hedland Mayor Kelly Howlett says a red alert means that people must not go outside until the all clear is given.
Authorities are most concerned about an expected storm surge along the coast overnight.
The Bureau of Meteorology says tides may rise significantly above normal high tide along the coast between Pardoo and Wickham, including Port Hedland.
Damaging waves and coastal inundation are expected, while heavy rain may cause flooding along the Pilbara region.
The cyclone has cut power to nearly 1,000 residents in Karratha and more than 170 residents in Port Hedland so far.
Authorities say they will remain without electricity until the area is clear.
There are also more than a dozen road closures in the area, while flights on Tuesday to centres including Karratha, Newman and Port Hedland have been cancelled.
On Monday night, Glenn Connell from Pyramid Station, 60 kilometres east of Roebourne, said he and his family had left the homestead to take shelter in their cyclone bunker.
"Oh it's howling, it's pretty fierce out there. The rain is pouring down and it's pretty windy," he said.
"The family is in the cyclone shelter, I built it quite a few years ago but we've never had one that's come over us so there's been no need to go into it."
Department of Fire and Emergency Services spokesman Les Hayter said earlier on Monday night that there had not been any calls for assistance, but he expects that may change once residents can assess the damage outside.
"The worst areas are certainly going to be in that path that's going to be swathed by this cyclone coming through from Whim Creek through the Paraburdoo, Tom Price area and then into the main part of WA," he said.