Belal Hossain, company commander of BGB-61 battalion, said a patrol team of BSF opened fire on a group of cattle traders when they went to the border to bring cattle around 10:30am.
Later, Indian police and BSF took away the body.
A letter was sent to BSF seeking return of the body after holding a flag meeting, said Belal.
In September, Indian Border Security Force had reiterated its policy of using non-lethal weapons on the Bangladesh-India border.
The BSF made the assurance in response to the concerns expressed by Border Guard Bangladesh (BGB) on border deaths.
The BSF assured that all unarmed and innocent trespassers and victims of human trafficking will be handed over to BGB personnel.