Barkov made his debut in SM-liiga with Tappara on 1 October 2011 and became the youngest player in the league to score a point, with his assist on a goal by Kalle Kaijomaa. The 37-year old record was previously held by Juha Jyrkkiö.

In December 2011, Barkov was chosen to play for Finland as the youngest Finnish player in the Ice Hockey World Junior Championships. During the quarter-final match on 2 January 2012 against Slovakia, Barkov became the second-youngest player to score a goal at the World Juniors at the age of 16 years and 4 months. The record is held by Kazakhstan’s Viktor Alexandrov, who set the record in 2001 at age 15.

On 15 July 2013, Barkov signed his first NHL contract with the Florida Panthers. He became the youngest player since the 1967 NHL expansion to score a goal on 3 October 2013, which he did it in a road game against Kari Lehtonen of the Dallas Stars at the age of 18 years and 31 days. Jordan Staal had previously held that record (for the post-expansion era), scoring his first NHL goal at the age of 18 years and 32 days.

In the midst of a successful 2015–16 season in which he was ultimately named a Lady Byng Memorial Trophy finalist (which he would lose to Anže Kopitar), on 26 January 2016, the Panthers signed Barkov to a new six-year, $35.4 million contract effective from the 2016–17 season through to the 2021–22 season.

In 2016, Barkov and then-Florida teammate Jussi Jokinen were selected to represent Finland at the 2016 IIHF World Championship. Finland won silver after a 2–0 loss to Canada. Barkov ended the tournament with nine points in nine games.

On 17 September 2018, Barkov was named the Panthers’ captain, replacing Derek MacKenzie. On 15 December, in a 4–3 overtime win over the Toronto Maple Leafs, Barkov scored his first career NHL hat-trick. He scored his second career NHL hat-trick on 17 February 2019 in a 6–3 win over the Montreal Canadiens. On 8 March 2019, in a 6–2 Panthers win over the Minnesota Wild, Barkov become the first Panther to record five assists in a one game. On April 18, for the third-straight season, Barkov was named a finalist for the Lady Byng Memorial Trophy, alongside Ryan O’Reilly and Sean Monahan. On 20 June, Barkov was named the winner of the trophy, accumulating just four minor penalties during the 2018–19 season.