A Montenegrin police source, quoted by the Reuters news agency, said the policeman, who was not in uniform at the time, was attacked by three men.
The shooting happened after a row in a restaurant near the capital, Podgorica.
The incident comes amid high tension ahead of Sunday's Yugoslav elections.
The pro-western government of Montenegro is boycotting the poll, prompting fears of a possible backlash by Belgrade.
A Montenegrin police source, quoted by the Reuters news agency, said the policeman, who was not in uniform at the time, was attacked by three men.
Reports say they had been arguing about politics before the attack.
A Yugoslav army spokesman, Colonel Slobodan Stojanovic, said the Montenegrin had fired the first shot.
The gunman is said to have been arrested in a Montenegrin village after the shooting.
He reportedly belonged to a battalion described by the Montenegrin Government as containing supporters of the pro-Belgrade Socialist People's Party.
A Yugoslav army spokesman, quoted by the Montenegrin news agency Montena-fax, named the Yugoslav policeman as Moma Mojasevic, and the dead officer as Nibojsa Lekovic.
Montenegro has vexed Belgrade with its attempts to forge its own path.
During the Kosovo conflict, the republic largely succeeded in distancing itself from the actions of President Milosevic.
It is boycotting Sunday's election, saying it will not be conducted fairly.
The state's reformist leader, Milo Djukanovic, has expressed fears that, after the poll, Montenegro could be under threat of action - either overt or covert - by Belgrade loyalists.