Martinsen, 26, had seven points (three goals, four assists) in 55 games for the Avalanche this season, and 18 points (seven goals, 11 assists) in 110 NHL games. He signed with Colorado as a free agent on May 15, 2015.
At 6-foot-3, 220 pounds, Martinsen is being counted on to add a physical presence to the Canadiens..
"I'm just going to play my game and bring some size and physicality and try to be a really good bottom-six player, obviously," he said. "Just go out there and work as hard as I can every game and help the team and bring some energy."
Andrighetto, 23, was selected in the third round (No. 86) by the Canadiens in the 2013 NHL Draft. He had eight points (two goals, six assists) in 27 games with the Canadiens this season and has 28 points (11 goals, 17 assists) in 83 NHL games since debuting for Montreal on Dec. 6, 2014.
"With his speed and hockey skill, he can help our power play,," Colorado general manager Joe Sakic said.