A fishing trawler capsized on the Naf River late Sunday evening local time, said Ariful Islam, commanding officer of the Bangladesh Border Guard in Teknaf, on the border with Myanmar.
Islam said his team rescued 13 people by pulling them from the water into their boats.
"They (were) so distressed," Islam said of those rescued. "We have provided them with first aid and food. Now they are in the camps."
He added it was unclear how many people were on board the boat or if any are still missing: "You never know, we might find more bodies."
The 12 dead bodies were found washed ashore near Shah Porir Dwip, on the southern tip of Bangladesh.
At least 519,000 Rohingya refugees have arrived in Bangladesh since late August after fleeing violence in Myanmar, according to the latest report
from the Inter Sector Coordination Group in Bangladesh.
Last week, Bangladesh announced plans to build a single, enormous refugee camp to house around 800,000 Rohingya refugees
as the flow of people across the border shows no signs of stopping.
"Solutions lie with (Myanmar) because the problem was created by the Myanmar government. We want them to take back their citizens to their own homeland," Obaidul Quader, a Bangladeshi minister, said last week, adding the refugees were an "unbearable burden" on his country.
In a new report released Friday, aid organization Refugees International described the actions of the Myanmar military as "crimes against humanity
Myanmar has repeatedly denied claims it is working deliberately to wipe out the Rohingya, saying they are carrying out counter attacks against "brutal acts of terrorism."
The crackdown in Rakhine intensified after Rohingya militants killed 12 security officers during coordinated attacks on border posts, according to Myanmar state media.
At midnight local time Monday (2:30 p.m. ET), a month-long ceasefire called by the militant Arakan Rohingya Salvation Army (ARSA) will come to an end, the group said in a statement Saturday.
ARSA leader Ata Ullah said the ceasefire was conducted to allow humanitarian access to Rakhine State and to allow safe passage for refugees to escape to Bangladesh.
He accused the Myanmar government of blocking humanitarian access, adding that ARSA is determined to "stop the tyranny and oppression waged against the Arakanese people."