Officials asked residents in the town of Denham, Shark Bay, 500 kilometres (311 miles) north of Perth to evacuate while sandbags were being made available to residents of Geraldton, further down the coast, due to potential storm surge.
The storm, which devastated parts of Indonesia and East Timor last week, brought lashing rain and winds of up to 170 kilometres per hour (105 mph) to areas officials said had not seen a tropical Cyclone in "decades".
The cyclones are hitting as India reels from a surge in coronavirus infections that has plunged the healthcare system into crisis and pushed the country's Covid-19 death toll above 300,000.
Cyclones are a regular menace in the northern Indian Ocean but many scientists say they are becoming more frequent and severe as climate change warms sea temperatures.
The Indian Meteorological Department said landfall began around 9am (0330 GMT) and warned that it would generate waves higher than rooftops in some areas. Coastal areas experienced wind gusts up to 155 kilometres an hour and pounding rain.
Rains have been pouring in six districts of the Indian Ocean island nation since Thursday night, and many paddy fields and roads have been inundated, blocking traffic.
Civil defence officials have warned that upwards of 317,000 people could be vulnerable to toxic gas emissions from the volcano under the current eruption's worst-case scenario.
About 228,000 people have been forced to seek emergency shelter due to flooding since June 2, the country's Ministry of Emergency Management said. Initial damages were estimated at more than $500 million, including the destruction of more than 1,000 homes.
Authorities warned it could cause extensive damage to flimsy houses and a storm surge could push seawater 25 kilometres inland, flooding cities including Kolkata.