The accident took place at a cantonment in central Tangail district when Border Guard Bangladesh (BGB) personnel were undergoing a firing training, said a local police official.
Army officials could not confirm the circumstances in which the mortar shell went off.
The Daily Star newspaper, quoting its sources, reported the mortar went off within the firing range, killing three BGB members.
The two military personnel, killed in the accident, were involved in management of the army-run field firing range, they said.