Barzal was selected 16th overall by the New York Islanders in the 2015 NHL Entry Draft. On September 10, he signed a three-year, entry-level contract with the Islanders. On October 15, 2016, Barzal made his NHL debut. He returned to the Thunderbirds and won the 2017 WHL championship as Barzal was named WHL Playoff MVP after registering 25 points in 16 games. Barzal's first NHL point came on October 15, 2017, against the Los Angeles Kings when he assisted on a goal by Josh Bailey. Barzal's first NHL goal came on October 19 against Henrik Lundqvist of the New York Rangers. Barzal's first multi-point NHL game came on October 26, 2017, when he had a goal and an assist playing against the Minnesota Wild. The goal, the second of his career, came in the waning seconds of the Islanders' 6–4 loss. Barzal's first NHL power play goal came on October 30 against the Vegas Golden Knights. Barzal set a franchise record for assists by a rookie when he recorded five assists on November 5 in a 6–4 Islanders win over the Colorado Avalanche. This also tied the franchise record for points in a game by a rookie. Barzal's first multi-goal game and his first hat-trick came on December 23, 2017, against the Winnipeg Jets in a 5–2 Islanders win. On January 13, 2018, in a 7–2 win over the Rangers, he became just the fifth player in NHL history to have two five-point games in a season before his 21st birthday. On February 9, 2018, in a 7–6 victory over the Detroit Red Wings, Barzal became the first NHL rookie to record three five-point games in a season since Joe Malone did so in the 1917–18 season. On April 7, Barzal tied the Islanders record for most assists by a rookie with 63. On April 22, Barzal was named a finalist for the Calder Memorial Trophy, which is awarded to the best rookie in the NHL. On June 20, he won the award.. Barzal and Kyle Okposo are the only players to lead the Islanders in scoring during John Tavares' nine-year tenure with the team, however Okposo did it in a season where Tavares was hurt, while Barzal did it in a season where they both played the full 82 games. Following the departure of Tavares during the 2018 off-season, Barzal began the 2018–19 season centering the Islanders' top line with Anthony Beauvillier and Josh Bailey. On December 29, Barzal scored a natural hat-trick in a 4–0 win over the Toronto Maple Leafs, becoming the first Islanders player to score a hat-trick against the Maple Leafs since Mike Bossy on March 20, 1986. On January 3, 2019, Barzal was named to the 2019 NHL All-Star Game. Barzal finished the season with 62 points, leading the Islanders in both points and assists. Barzal won the fastest skater competition at the 2020 NHL All-Star Skills Competition.
Barzal speaks fluent French, having taken French immersion in school, and as a result, he has a very close friendship with Islanders teammate Anthony Beauvillier, whom he met when the two played for Canada at the 2015 World U18 Championship.
