Service, 28, has recorded seven points (one goal, six assists) in 28 games for Nashville this season while averaging more than 20 minutes per game.
Selected in the fourth round of the 2015 NHL draft, Service has spent his entire 245-game career in Nashville.
It’s unclear when he’ll make his Montreal debut, as he’s been on injured reserve with an upper-body injury since Dec. 7.
Barron, 23, has been limited to just one point (one goal) in 17 games with the Canadiens this season.
He joined Montreal on March 21, 2022, in the deal that sent forward Arturri Lehkonen to the eventual Stanley Cup champion Colorado Avalanche.
In 111 career games with the Canadiens, Barron has produced 31 points (13 goals, 18 assists).
The NHL’s Christmas roster freeze, which prevents trades, runs from Dec. 20-27.