During his tenure with the team, he earned the Wayne Gretzky 99 Award as playoff MVP before beginning his professional career with the St. Louis Blues.

He soon surpassed his older brother when he was enrolled in youth hockey programs and began playing with the year above his in the Minor Atom Mississauga Senators.

[13] Upon returning from the tournament empty handed, Fabbri was selected to replace Rebels' first line during a 6–3 win over the Windsor Spitfires, where he recorded one assist.

[15] As a result of his successful rookie campaign, Fabbri was invited to compete with the Canadian National U18 team at the 2013 Ivan Hlinka Memorial Tournament.

[21] The Storm beat the Whalers and Fabbri went on to record 28 points in 16 games to help the team win their third J. Ross Robertson Cup in franchise history.

[23] Prior to his selection, he stated that he'd enjoy studying business at the University of Guelph after graduating from Our Lady of Lourdes Catholic School.

[24] On September 3, 2014, Fabbri signed a three-year, two way entry-level contract with the Blues but returned to the Storm for his final year of major junior hockey.

[25] He was invited to participate in the 2015 World Junior Ice Hockey Championships where he suffered an ankle injury during the quarter-finals against Denmark[26] and was held to only 30 games for the OHL season.

[27] At the conclusion of the 2014–15 season with the Storm, Fabbri was reassigned by the Blues to their American Hockey League (AHL) affiliate, the Chicago Wolves, on April 15, 2015.

Blues' Head Coach Ken Hitchcock praised Fabbri's goalscoring ability by saying "If you look at his goals, there’s maybe one that the goalie could have saved.

[40] Shortly after reaching the 15-goal mark, Fabbri suffered a lower body injury as a result of a cross-check from Colorado Avalanche forward Jack Skille and was listed as day-to-day.

[42] The Blues qualified for the 2016 Stanley Cup playoffs and Fabbri helped the team beat the Chicago Blackhawks during the Western Conference First Round.

Midway through the first period, he suffered a torn ACL in his left knee and was out for the remainder of the regular season and 2017 Stanley Cup playoffs.

"[50] Fabbri also attended the Blues' training camp where Head Coach Mike Yeo said he "looked good...He's skating, he's shooting, he's doing the things you hoped he could do and is showing his skill level… We've got a lot of belief in Robby and in his capabilities.

"[51] In spite of this, he was reassigned to their AHL affiliate the San Antonio Rampage on a conditioning assignment, with the expectation he would rejoin the Blues eventually.

Fabbri recorded one goal in ten postseason games[1] to help the Blues defeat the Boston Bruins to win the 2019 Stanley Cup.

[58] Fabbri re-joined the team for their 2019–20 season[59] and played nine games for them before being traded to the Detroit Red Wings in exchange for Jacob de la Rose on November 6, 2019.

He first suffered a lower-body injury during a game against the Boston Bruins on February 9,[64] and was then reinjured after colliding with New Jersey Devils forward Jack Hughes.

[75] Fabbri was traded to the Anaheim Ducks along with a conditional fourth round 2025 draft pick (either Boston or Detroit's own selection) on July 3, 2024, by the Red Wings in exchange for goaltender Gage Alexander.