Suzuki was taken by the Vegas Golden Knights in the first round (No. 13) of the 2017 NHL draft. He was traded to the Montreal Canadiens Sept. 18, 2018 in the Max Pacioretty trade. He was named the 31st captain of the Canadiens on Sept. 12, 2022, at 23-years-old to become the youngest in team history. Hockey Hall of Fame defenseman Sylvio Mantha was named captain at age 24 to begin the 1926-27 season.

The London, Ontario, native signed an eight-year, $63 million contract Oct. 12, 2021, and had 61 points (21 goals, 40 assists) in 82 games that season.

Suzuki scored the 100th goal of his NHL career 17 seconds into overtime of Montreal's 4-3 win against the Nashville Predators at Bridgestone Arena on March 5. He made his NHL debut against the Carolina Hurricanes on Oct. 3, 2019, and got his first NHL point with a power-play assist in a 5-4 overtime loss to the Buffalo Sabres on Oct. 9. He scored his first NHL goal in a 4-0 victory against the Minnesota Wild on Oct. 17.

His assist on Cole Caufield’s first goal in Montreal's 7-5 win at the Buffalo Sabres on Nov. 11, 2024, was his 300th NHL point in his 389th game, the fourth-fewest by a Montreal player in 35 years to reach the mark after Stephane Richer (336), Saku Koivu (381) and Chris Chelios (385). The following season, Suzuki helped Team Canada win silver at the Olympic Winter Games Milano Cortina 2026.

Suzuki had a goal and an assist a 4-1 win at the New York Islanders on April 12, 2026, to become the fifth player in the 108-year history of the Canadiens with at least 100 points in a season, joining Guy Lafleur (six times), Peter Mahovlich (two times), Mats Naslund and Steve Shutt. His 29th multipoint game was the most by a Canadiens player in a season since Naslund in 1985-86 (31). He was named a finalist for the 2026 Selke Trophy, awarded annually to the forward voted best to excel in the defensive aspects of the game, after finishing plus-37, sixth in the NHL with 1,449 face-offs taken, winning 50.4 percent and averaging 20:49 of ice time per game, tops among Montreal forwards.

The speedy center made the Ontario Hockey League First All-Rookie team in 2015-16 after scorings 38 points (20 goals, 18 assists) for Owen Sound. The next season for Owen Sound, Suzuki had 96 points (45 goals, 51 assists), made the OHL All-Star second team and won the William Hanley Trophy for sportsmanship. After spending time in the Golden Knights' training camp before the 2017-18 season, he returned to Owen Sound and scored 100 points (42 goals, 58 assists). He also won the Hanley Trophy again.

Suzuki capped his junior hockey career with a championship. He scored 94 points (34 goals, 60 assists) splitting the season between Owen Sound and Guelph and won a third straight Hanley Trophy. Het set a Guelph record with 42 points (16 goals, 26 assists) in the 24 playoff games to win the Wayne Gretzky 99 Award as playoff MVP. Guelph defeated Ottawa in the championship series.