Bangladesh on Wednesday rebuked Myanmar for opening fire on a boat in the Naf river that marks their border and killing one fisherman, describing it as an "act of unprovoked aggression".
Tensions have been running high since thousands of Rohingya began pouring over the border, fleeing a crackdown by the Myanmar army which began in October.
It was the second time that Myanmar forces had fired on Bangladeshi fishermen.
Bangladesh's foreign ministry expressed "deep concern" at the latest shooting on Monday, which also seriously injured another crewman aboard the trawler.
"The ministry urges the government of Myanmar to ensure that Myanmar desist from repeating such an act of aggression," a statement said.
Police said Myanmar border guards opened fire without warning on the fishing boat when it unintentionally strayed into Myanmar waters.
Nearly 70,000 Rohingya Muslims have entered Bangladesh in recent months, with stories of killings and mass rape by Myanmar soldiers that have raised global alarm and sparked protests around Southeast Asia.
The army says it is hunting militants who mounted deadly raids on police posts in October.
According to the Bangladesh government some 400,000 Rohingya are living in Bangladesh and most are unregistered.
Dhaka last week asked diplomats and UN agencies to support a controversial plan to relocate Rohingya refugees to a remote island.