A Bangladeshi border guard was wounded and another is being held by Myanmar after troops from the two countries exchanged fire on Wednesday, paramilitary officers and witnesses said.
The local director of operations for Border Guard Bangladesh, Ekram Khan, said the shoot-out was "the outcome of a total misunderstanding" - an assessment that chimed with witness reports.
Local fishermen said a Bangladeshi patrol boat on the Naf river which divides the two countries came under fire from Myanmar border guards, who had apparently mistaken them for smugglers.
The area where the shoot-out occurred is notorious for people smuggling between the two countries, which have come under the spotlight over a migrant crisis in recent weeks. But clashes between border forces are rare.
One sustained multiple bullet wounds during the clash in Bangladesh's south-eastern district of Cox's Bazar.
"Our soldiers started firing in retaliation and private Biplob Kumar sustained injuries to his head and right hand," said Abu Russell Siddiki, a spokesman for the Bangladesh force.
Another Bangladeshi border guard, Abdur Razzak, was taken by Myanmar Border Guard Police to a border force camp.
Khan said the issue would be resolved at a flag meeting whose timing had yet to be confirmed.
People smuggling is rife in Cox's Bazar and many former fishermen have joined smuggling rings because they are so lucrative.
The scale of the issue was thrown into relief when thousands of migrants, most of them Rohingya from Myanmar or economic migrants from Bangladesh, were stranded in Southeast Asian waters last month.
The crisis followed a Thai crackdown on people smuggling that threw the multi-million dollar industry into disarray, leading gangmasters to abandon their victims on land and at sea.