The border guards of Bangladesh and Myanmar fired at each other's patrols on the Naf river along the border in Bangladesh's Cox's Bazar, 391 km southeast of capital Dhaka.
The exchange of fire between the two sides was reported early on Wednesday, according to Xinhua news agency.
Myanmar Border Guard Police (BGP) reportedly opened fire at a patrol trawler of Border Guard Bangladesh (BGB) in mid-river in Teknaf and also abducted one of its members.
The firing was effectively retaliated by BGB troops.
Bangladeshi State Minister for Home Asaduzzaman Khan Kamal told journalists here that a "misunderstanding" led to the exchange of fire between the border patrols of Myanmar BGP and BGB.
He said shooting erupted as the BGP mistook Myanmar BGB men to be smugglers or human-traffickers.
"Through a flag meeting the abducted BGB nayek Abdur Razzak, 40, would soon be brought back to the country," he said.
The incident left a BGB soldier wounded, he added.
