Hundreds of people rushed through a small gate into a factory compound before dawn to get the free garments, causing a crush.
Police have detained seven people, including the owner of the factory.
During the Muslim holy month of Ramadan, wealthy Bangladeshis often donate clothing to the poor.
Police told AFP news agency that 1,500 people had gathered outside the chewing tobacco factory at about 04:45 local time (22:45 GMT Thursday) after the owners announced they would distribute free clothing,
The stampede erupted when people tried to force their way in.
Television pictures showed scenes of devastation, with hundreds of blood-spattered sandals lying at the factory gate, which was named by local media as Nurani Jorda.
?Most of the dead are poor and emaciated women,? Mymensingh police chief Moinul Haque told AFP.
Police said they expected the death toll to rise.