The boat, called 'Silver Star' in Burmese, sank Friday evening in a river near Pathein, a port city west of commercial capital Yangon.
It was believed to be carrying around 60 passengers on their way home from a wedding ceremony, according to a local police officer.
Of the dead, officials said 16 were women and four were men.
"They were crossing to the other side of the river after attending a wedding in Pathein. Most of them were relatives from the same village," said the policeman, who requested anonymity.
Both ships were unlit when they collided in the middle of the river, he added.
"We estimate nine people are still missing," regional MP Aung Thu Htwe told AFP, adding that some 30 people had been rescued alive the night before.
Local media photos showed frenzied scenes as rescuers worked in the dark Friday night to wheel stretchers away from the river and lay bodies onshore.
"We will do search and rescue for the whole day," he told AFP.
Fatal boat accidents are common in Myanmar, a poor country with rudimentary transport and weakly-enforced safety regulations.
Vessels ferrying people along the country's coastline and rivers are often dangerously overcrowded, and accidents can have staggering death tolls. It can also take several days for all bodies to be retrieved.
Last October 73 people, including many teachers and students, drowned when their overloaded vessel capsized in central Myanmar on the Chindwin River.
Around 60 people also died in March 2015 when their ferry sank in rough waters off of Myanmar's western Rakhine state.
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