Internationally Fiala has played for the Swiss national team at several tournaments, both at the junior and senior level, and has appeared in two World Championships.

Fiala played in the 2009 Quebec International Pee-Wee Hockey Tournament with the Swiss Eastern team.

[1] He later played in various junior leagues in his native Switzerland prior to joining the Swedish club Malmö Redhawks for the 2012–13 season.

He was praised by Head Coach Ulf Dahlén for his play following his SHL debut, a 5–4 defeat to Linköpings HC.

[4] Prior to joining the senior team in the SHL, Fiala had been one of the top scorers in the junior league, with 10 goals and 25 points in 27 games.

[5] Fiala was ranked as one of the top European prospects for the 2014 NHL Entry Draft, being considered a top-three player by many scouting services; he ultimately was selected by the Nashville Predators 11th overall.

[14] On 29 June 2022, Fiala as an impending restricted free agent was traded by the Wild to the Los Angeles Kings in exchange for defenseman Brock Faber and a first-round pick in 2022.

Fiala played in the Ivan Hlinka Memorial Tournament in 2012 and 2013 as a member of the Swiss U18 national team.

He also skated for his country at the 2014 World Junior Ice Hockey Championships, where he was lauded as one of the key players on the Swiss roster.