Cyclone Giri hit western Rakhine state on Friday packing winds of up to 110mph (177km/h), with the major town of Kayaukpyu hard hit.
There are unconfirmed reports of dozens of villagers and fisherman missing but the military rulers have given no estimate of casualties or damage.
Aid groups have set up temporary camps to shelter more than 5,000 people.
Residents in Rakhine (also known as Arakan) say they are facing a shortage of drinking water and food after flood waters and falling trees destroyed homes.
Communications have also been hit, with power lines and telephone poles badly damaged, reports say.
More than 130,000 people were killed when Cyclone Nargis struck the Irrawaddy Delta in May 2008.
The military government was widely criticised for what was described as an inadequate warning and initial response to the disaster.
However, state-run media have provided coverage of Cyclone Giri.
There has been no official announcement about the scale of the damage or any casualties.
The worst-hit coastal areas included Kayaukpyu, Myebon, Pauktaw, Myanaung, and Ponnagyu, where many poor families live in huts made from bamboo.
Three temporary camps have been set up in Kayaukpyu by the Myanmar Red Cross and the Social Welfare Ministry, said Andrew Kirkwood, of aid group Save the Children.
On Kyunthaya island, located between Myebone and Kayaukpyu, only seven houses out of 622 houses were still standing, Mr Kirkwood was quoted by the AP news agency as saying.
"The whole town of Kayaukpyu has been hit hard," a local resident told The Irrawaddy, which is based in Thailand.
"There are fallen trees everywhere, and many houses right on the coast have been swept away. All the shops are closed, so there's nowhere to buy food or drinking water."
Meanwhile, there are reports of a fire at an oil pipeline in central Burma. It was not immediately clear if there were any casualties.
Thousands of people have been displaced in Burma following a powerful cyclone, residents and aid agencies say.