Here's the deal ... cops say they responded to Nashville Crossroads bar in downtown Nashville, Tenn. after they received a call about an altercation with patrons.

Once officers arrived on scene ... they say witnesses told them 46-year-old Barnaby, his girlfriend and other bar-goers had gotten into a scrap, when Matthew began choking a bouncer.

Cops say they noticed "a strong odor of an alcoholic beverage" on Barnaby's breath when they went to talk to him and say he had watery eyes and slurred speech.

Cops add the bouncer wished to press charges against the former Dallas Stars winger for the alleged choking incident ... so they arrested Matthew.

Barnaby was booked and charged with assault and public intoxication. He has a court date to face the charges set for later this month.

Of course, Barnaby was no stranger to altercations in his NHL career ... he was in dozens of on-ice fights and is known as one of the league's best all-time enforcers.

This also isn't Barnaby's first brush with the law ... ESPN famously fired the hockey analyst after he was arrested for drunk driving in 2011.