A joint navy and coast guard patrol boat detained the trawler near Bangladesh's southernmost island of St Martin's close to the border with Myanmar, an official said.
"There were 116 illegal migrants in the fishing trawler. They are all Bangladeshis," coast guard station commander Dickson Chowdhury told AFP by phone.
Many had been stuck on the trawler for weeks off the Bangladesh coast waiting to begin the perilous journey to Southeast Asia, and many had gone without food for days, Chowdhury said.
"They have been on the boat from 15 days to three months. For the last seven days some of them have not eaten anything other than water. Some were found in emaciated condition," he said.
Chowdhury said the crew, thought to be Myanmar nationals, had abandoned the trawler on Tuesday morning after being spotted and chased by Bangladeshi border patrol boats.
Officials said the migrants had come from all over impoverished Bangladesh for the journey to Malaysia in search of a better life.
"There are 16- and 17-year-old boys in the ship as well as a 60-year-old man," Chowdhury said.
Another coast guard official said navy and coast guard patrol boats detained the trawler at 5:30pm.
"We learnt that it was heading to Malaysia with the illegal migrants," al Imran, of the coast guard's press department, said.
The discovery comes after nearly 2,000 boat people from Myanmar and Bangladesh were rescued or had swum to shore in Malaysia and Indonesia in recent days.
The spate of arrivals comes as Thailand, a key stop on a Southeast Asian people-smuggling route, cracks down following the discovery of mass graves that has laid bare the extent of the thriving trade.
Thousands of Bangladeshis and ethnic Rohingya refugees from Myanmar attempt the journey to Malaysia every year, mainly from Bangladesh's southern coastal town of Teknaf, which borders Myanmar's western Rakhine coast.
They pay up to $3,000 to human traffickers who lure them with hopes that high-paying jobs are waiting for them in Malaysia, which is like Bangladesh a Muslim-majority nation.
Rights groups say thousands have perished attempting the 3,200-kilometre journey to Malaysia, with many falling into the hands of people-traffickers.
Last week Bangladesh's police and border forces launched a crackdown on human traffickers after the discovery of the graves in Thailand.
Five traffickers, accused of smuggling thousands of migrants, were shot dead and five more were arrested.
Bangladeshi police have said they have rescued more than 3,000 people from Cox's Bazaar and Chittagong city from the hands of traffickers over the past five years.
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