The 24-year-old Chicago native has played 84 NHL games since debuting with the Wild in 2015-16. This season, Reilly has registered two goals and 10 points in 38 games.
His father, Michael J. Reilly, was drafted in the eighth round by the Canadiens in 1977, but he never played an NHL game.
The University of Minnesota product represented the United States on two occasions internationally, winning gold alongside Alex Galchenyuk at the 2013 World Junior Hockey Championship and securing a bronze medal at the World Hockey Championship in 2015.
The 6-foot-2, 193-pound puck-moving defenseman has four goals and 18 points over the course of his career. He was a fourth-round pick, 98th overall, of the Columbus Blue Jackets in 2011.
The Canadiens now have six draft picks in the 2019 NHL Entry Draft.