Prior to his NHL career, Barabanov played for SKA St. Petersburg in the Kontinetal Hockey League (KHL), dating back to the 2013-14 season. In his KHL career, Barabanov recorded 137 points (62 goals, 75 assists) in 262 games. He was named to the KHL All-Star game in 2018-19, and also earned KHL Forward of the Week honors on Feb. 25, 2019. He set a career-high in goals, assists and points during the 2018-19 season, scoring 46 points (17 goals, 29 assists) for St. Petersburg. Barabanov ranked second on the team in points, third in assists, and fifth in goals.
Internationally, Barabanov has represented Russia in the 2014 World Junior Championships, 2017, 2018 and 2019 World Championships, and 2018 Olympic Games. He helped Russia win Bronze in 2014, 2017 and 2019 and won a Gold Medal in the Olympics. He appeared in six games, scoring two points in the tournament.
The five-foot-ten, 192-pound native of St. Petersburg, Russia was originally signed by Toronto as a free agent on April 7, 2020.