The bus was carrying around 40 passengers from central Bago province when it plunged off a highway near Myawaddy, a town on the Thai border, on Friday.
"Nineteen people were killed and 21 people were injured, while a few people were lucky to live," Kyi Lin, the chief of police in Karen state, told AFP.
"(The bus) fell down into a narrow and deep gorge," he said, adding that police believe the driver lost control of the bus because of a brake failure.
Police and local aid groups have brought the injured to nearby hospitals for urgent care and are making funeral arrangements for the dead, he added.
A hospital in Mae Sot, the Thai town across the border, took in seven patients from the crash who were in "critical condition," a medical worker told AFP.
Road accidents are common in impoverished Myanmar, whose transport network is in poor condition after decades of underinvestment by the junta that ruled the country for almost half a century until early 2011.
With 20.3 road fatalities per 100,000 people, Myanmar has the second most dangerous roads in Southeast Asia, according to data collected by the World Health Organization in a 2015 report.
Despite its relatively good infrastructure, neighbouring Thailand has an even worse road safety record.
The WHO estimates about 24,000 people die each year in traffic accidents on Thai roads.
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