The victim was identified as Sumon Ali, 22, a native of Moralpara village in Shibganj Upazila.
His body was found on the Bangladeshi side of the Shingnagar border early Monday, according to Shibganj Police OC Shamsul Alam said.
"The body has been sent to the Chapainawabganj Sadar Hospital for an autopsy," OC Shamsul said.
The Border Guards Bangladesh and village police personnel said that Sumon was gunned down by the BSF.
Sumon and a few others had gone near the Indian border to bring back their cattle when a BSF patrol opened fire on them, according to some locals.
A wounded Sumon died while carried away from the area by his companions, who later left his body on a road in Chayarashia village and fled, they said.
A body was found in the Bangladesh territory about 3km away from the zero line of the border, according to Lt Col Suruj Mia, captain of BGB's Chapainawabganj 53 Battalion.
"We contacted his family after identifying the body. Sumon had left his house on Sunday evening."
“An investigation is being conducted to identify Sumon's assailants. We have contacted the BSF about a meeting over the incident,” he added.