Damrey was downgraded into a tropical depression as wind speeds dropped to just 38 kilometrees (23 miles) per hour from a high of around 200 kilometres per hour, according to the Hong Kong Obseravatory.
The storm claimed four lives in Vietnam on Tuesday, weather officials said. It also killed 16 people in southern China and 16 others in the Philippines.
After passing over northern Vietnam, the storm brought heavy rain and strong winds to Laos. Witnesses said the streets of the Lao capital Vientiane were turned into a muddy quagmire on Wednesday and that phone connections were disrupted.
Reports of damage were not immediately available, but the Vientiane Times said winds of up to 100 kilometres per hour had struck the country's central provinces late on Tuesday.
A Vietnamese government weather official said the typhoon had weakened after entering Laos.
It killed two people each in Vietnam's northern provinces of Nam Dinh and Thanh Hoa, and left 13 people injured. About 300,000 people were evacuated from coastal regions where extensive networks of dykes were breached.
"According to initial estimates, Damrey, the most violent storm to hit Vietnam in a decade, caused damage worth tens of millions of dollars," a central weather official said.
China's Civil Affairs Ministry said the storm had caused nearly 8.5 billion yuan (1.05 billion dollars) in damage in Hainan, Guangdong and Guangxi provinces as of Monday night, while 436,000 people had been evacuated.
Hainan Vice Governor Wu Changyuan said that 20,000 homes had been flattened on the island province, while 380 kilometers (228 miles) of roads had been damaged and 704,000 hectares of cropland ruined, Xinhua news agency said.
By Tuesday evening, Xinhua put economic losses at 10 billion yuan and the death toll at 16.
In the Philippines, the storm killed 16 people and displaced more than 8,000 people in the Bicol peninsula southeast of Manila. Several hundred hectares of farmland were flooded.
A Vietnamese civil aviation official said 10 flights from the Noi Bai international airport in Vietnam's capital, Hanoi, were cancelled or delayed on Tuesday, leaving about 1,000 passengers stranded.
The region is prone to tropical storms and typhoons, two of which caused widespread destruction and killed scores of people this season.