The boat was carrying an estimated 50 people when it went down in the estuary of the Naf river that divides the two countries, Border Guard Bangladesh (BGB) area commander Lieutenant Colonel S.M. Ariful Islam told AFP.
Nearly 200 Rohingya have drowned over the last six weeks making the perilous crossing into Bangladesh, many in small wooden fishing boats that are dangerously overloaded.
They are fleeing violence in Myanmar's sectarian-plagued Rakhine state where the United Nations has accused troops of waging an ethnic cleansing campaign against the Rohingya Muslim minority.
Islam said the bodies of the eight confirmed victims had washed up on the river banks, while 21 survivors had swum to safety.
Coast and border guards were conducting a search and rescue operation in the Naf river, he said.
More than half a million Rohingya have arrived in Bangladesh over the last seven weeks to escape a military crackdown that the the UN has said amounts to ethnic cleansing.
The stateless Muslim minority has faced decades of persecution in mainly Buddhist Myanmar.
The latest influx began in late August after attacks by Rohingya militants on police posts in Myanmar.
Another border guard told AFP the boat sank was just 200 yards (metres) from the Bangladesh coast when it sank in rough waters.
Fazlul Haq, a local official, said the boat was owned by a Bangladeshi villager who had made large amounts of money ferrying Rohingya into the country.
He said the small fishing trawlers were highly vulnerable to accidents as they approached the shore, where they are often battered by large waves.
Refugees are often charged exorbitant fees for the trip.
The latest accident came a week after another boat packed with Rohingya refugees capsized in the area, killing at least 34 people.
