Fiala, a native of St. Gallen, Switzerland, and chosen by the Nashville Predators in the first round (No. 11) of the 2014 NHL Draft, scored two overtime goals in the Stanley Cup Playoffs before his 21st birthday.

In his first 18 playoff games with Nashville, Fiala scored five goals. In the fourth playoff game of his NHL career, he scored 16:44 into overtime in Game 3 of the Western Conference First Round against the Chicago Blackhawks on April 17, 2017, giving Nashville a 3-2 win and a 3-0 series lead en route to a sweep.

The Predators advanced to the Stanley Cup Final in 2017, but Fiala sustained a broken femur in the second round against the St. Louis Blues and missed the remainder of the postseason.

He returned healthy in 2017-18 and had NHL career highs in goals (23), assists (25), points (48), plus-minus (plus-20), power-play points (13) and games played (80). Fiala again showed his playoff prowess in Game 2 of the Western Conference Second Round against the Winnipeg Jets, scoring in the second overtime of Game 2 for a 5-4 win that evened the best-of-7 series at 1-1.

But after a slow start to the 2018-19 season, the Predators traded him to the Minnesota Wild on Feb. 25, 2019. Ironically, his first two goals for Minnesota came against the Predators on March 5.

Fiala had 85 points (33 goals, 52 assists) in his fourth season with the Wild before he was traded to the Los Angeles Kings on June 29, 2022. The next day he signed a seven-year, $55.125 million contract with the Kings, preventing him from becoming a restricted free agent. He had six shots on goal in 21:12 of ice time in his 600th NHL game, a 3-2 loss at the Pittsburgh Penguins on Dec. 17, 2024.

Fiala won a silver medal with Switzerland at the 2018 IIHF World Championship with five points in five games. He was named to represent Team Switzerland at the Olympic Winter Games Milano Cortina 2026.