During his junior career in the Ontario Hockey League (OHL), he won the Wayne Gretzky 99 Award as playoff MVP in 2013, as well as two J. Ross Robertson Cup titles with the London Knights.

His Chiefs coach Rob Simpson described Horvat as a player who "put up a ton of points and maybe cheated [defensively] a little bit at times".

[11] Joining the Knights for the 2011–12 season, Horvat scored his first OHL goal in his league debut, an 8–0 win over the Saginaw Spirit on September 23, 2011.

[12] During his rookie year with London, Horvat scored 11 goals and recorded an additional 19 assists, and he posted a +27 plus–minus through 64 regular season games.

The Knights defeated the Barrie Colts 3–2, and Horvat received the Wayne Gretzky 99 Award for the most valuable player in the OHL playoffs.

[19] Although the Knights lost to the Portland Winterhawks during the semifinal round of the 2013 Memorial Cup,[20] Horvat, who had five points in as many games and did not record any penalty minutes, was awarded the George Parsons Trophy for the most sportsmanlike player during the tournament.

[21] Leading into his professional draft year, the NHL Central Scouting Bureau ranked Horvat the 15th-most valuable hockey prospect in North America.

The acquisition of Zac Dalpe and Jeremy Welsh from the Carolina Hurricanes gave the Canucks enough roster depth that they could send Horvat and fellow draft pick Hunter Shinkaruk back to their respective junior teams.

[28] Competing for an NHL roster spot in his second training camp with the Canucks the following season, Horvat was hit by Edmonton Oilers forward Tyler Pitlick during a pre-season game and suffered a shoulder injury.

[29] Upon recovering, he was assigned to the Canucks' American Hockey League (AHL) affiliate, the Utica Comets, on a conditioning basis.

His season play earned him two fifth-place votes for the Calder Memorial Trophy, ranking him 11th among first-year players for the rookie of the year award.

During the first half of the 2015–16 season, Horvat juggled heightened goal-scoring expectations along with increased defensive responsibility after injuries to Brandon Sutter and Henrik Sedin.

Horvat credited this change to advice from his father to shoot the puck more often, in lieu of bull-rushing the net,[38] in addition to increased chemistry with left-winger Sven Bärtschi.

[40] On March 3, 2017, Horvat was named as one of Vancouver's second alternate captains, replacing longtime Canuck Alexandre Burrows.

Horvat ended the 2016–17 season playing in all in all 82 games with 20 goals, 32 assists and 52 points recorded, setting career highs in all three categories.

[49] On January 30, 2023, Horvat's nine-season tenure with the Canucks came to an end when he was traded to the New York Islanders, in exchange for Anthony Beauvillier, Aatu Räty and a conditional first-round pick in 2023.

Because Horvat is slightly older than Konecny, the two did not play minor hockey together, but would regularly face each other throughout their junior and professional careers.

[61] Horvat's younger brother Cal also played for the Elgin-Middlesex Chiefs and London Knights before deciding to become a police officer in Ontario.