Shaw also played for the Montreal Canadiens prior to the end of his career in 2021 due to suffering multiple concussions.

Shaw had 17 points (eight goals and nine assists) overall in his OHL rookie season and ranked second on his team with 97 penalty minutes (PIM) in 56 regular-season games.

During the 2010-11 season, Shaw led Owen Sound with 135 penalty minutes and ranked fifth on the team with a junior career-high 54 points.

This season gave him junior career highs, with 54 points, 22 goals, 32 assists, 135 penalty minutes in 66 regular-season games.

In Rockford's 5–3 win against the Peoria Rivermen on October 9 at Carver Arena Shaw made an assist on the game-winning goal, his first professional career point.

Shaw scored two goals in Rockford's 5–4 shootout loss to Grand Rapids Griffins on December 14 at Van Andel Arena.

He needed stitches, but later returned to score the first goal of his NHL career on his first shot of his first game against Ilya Bryzgalov and played on the Blackhawks first line with Patrick Sharp and captain Jonathan Toews.

[6] On January 18, Shaw recorded his first career assist on a goal by Jonathan Toews in a game against the Buffalo Sabres.

He served a six-game suspension after leaving the bench to join a fight in a game against the Lake Erie Monsters on November 3, 2012.

On June 12, 2013, Shaw had the game-winning tip-in of the opening game of the Finals to give the Blackhawks a 4–3 triple-overtime victory over the Boston Bruins.

Officials stopped the play and Shaw was helped to his feet by teammates Nick Leddy and Michal Rozsíval and repaired in the dressing room by the trainers.

[16] Shaw played all 23 playoff games and scored nine points (five goals, four assists) and continuing on the third line role with Brandon Saad and Viktor Stålberg.

Shaw finished the 2015–16 season playing in 78 games with 14 goals, 20 assists and 34 points and was again the team leader in penalty minutes with 69.

Later in the same game, he shouted a homophobic slur towards a referee who had penalized him for interference against Blues defenseman Jay Bouwmeester and also instigated a brawl after the final horn.

[18] Shaw apologized for the remarks the next day during a press conference at O'Hare International Airport moments before the Blackhawks boarded their flight to St. Louis for game five.

[22] On June 24, 2016, Shaw was traded to the Montreal Canadiens during the 2016 NHL Entry Draft in exchange for two 2016 second-round picks.

[26] On December 12, Shaw sustained a concussion after being upended on a hit by Boston Bruins defenseman Torey Krug, causing him to miss 14 games.

On November 24, 2018, Shaw recorded his 100th NHL assist on a goal by Tomáš Tatar in a 3–2 loss to the Boston Bruins.

[36] As a result of his rejuvenation, Shaw was nominated by the Canadiens for the Bill Masterton Memorial Trophy, the award that goes to the player that "best exemplifies the qualities of perseverance, sportsmanship and dedication to hockey" but was not named a top three finalist by the league.

[42] On April 26, towards the end of the season, Shaw announced his retirement effective immediately after being advised by the team doctors to discontinue his playing career due to multiple concussions within short time spans.

[46] He compared his playing style to Boston Bruins player Brad Marchand, whom he fought in the third game of the 2013 Stanley Cup Finals, by saying "We're both agitators.

[51] In August 2013, Shaw auctioned the stitches from his facial injury—made famous as "the definitive image of the NHL playoffs"[52]—for $6,500 and donated the money to The V Foundation for Cancer Research.

[55] In May 2023, on the Raw Knuckles Podcast with Chris Nilan and Tim Stapleton, Shaw discussed the alleged sexual assault of Kyle Beach, which happened during the Blackhawks' 2009–10 season.