Bangladeshi border forces say two of their guards have been shot dead by Indian troops near a frontier post.
The incident took place in the north-western district of Chapainawabganj on Thursday night, officials say.
Bangladesh Rifles chief Maj Gen Shakil Ahmed said Indian troops had fired without provocation near the border.
India said its troops had been chasing cattle smugglers and that both sides' forces had traded heavy fire. One Indian soldier was seriously injured.
Locals said Indian troops had opened fire on the cattle smugglers, perhaps without informing the Bangladeshi border force.
The incident comes a day after the two countries' foreign secretaries met in Delhi.
The two countries share a long and porous border which is not properly demarcated. Over the past decade they have regularly exchanged shelling and small arms fire over the frontier.
Correspondents say that such incidents have not seriously interfered with generally friendly relations between Delhi and Dhaka.
However, tensions increased in 2006 when India began fencing off the 4,000km (2,500-mile) border to keep out what it described as illegal immigrants and "cross-border insurgents".