Cyclone Giri strengthened just before making landfall near the city of Sittwe, state media reported, affecting thousands of people and destroying 2,800 homes, two bridges and dozens of government buildings.
The category four storm hit several areas of western Rakhine state including Myebon, Pauktaw, Myanaung, Ponnagyu and Kyaukphyu.
It initially struck land on Friday in Rakhine with winds of up to 193 kms per hour.
The coastal town of Kyaukphyu was the worst-hit, with the power cut off and the sea wall partly destroyed.
Poor families living in bamboo huts populate the costal area.
The government is yet to make any statement on damage or casualties.
The Myanmar Red Cross and the Social Welfare Ministry has set up three makeshift camps in Kyaukphyu town to house about 5,000 people.
A Red Cross worker in the former capital Yangon estimated that about 70 per cent of Kyaukphyu town was destroyed, with about 60,000 people in the district needing assistance.
"Fishermen and people there have had time to move to safer places as disaster measures were already in place," he said.
"Our office in Kyaukphyu was destroyed by a falling tree ... we have had problems getting transport and the latest data but are trying to reach the affected areas as soon as possible."
After hitting the coast, the storm headed northeast through the central part of the country.
Myanmar is frequently hit by tropical storms and in 2008 was battered by Cyclone Nargis, which left 138,000 people dead or missing, mostly in the southwest delta region.
Nargis unleashed winds of 240kph and storm surges up to four metres high, sweeping away thousands of homes, flooding rice fields with salt water and ravaging schools and hospitals.
Myanmar's military government faced international criticism for its response to the disaster.
It was accused of blocking emergency aid and initially refusing to grant access to humanitarian workers and supplies.