Arvidsson had success right away, winning a silver medal in 2008-09 with Swedish club Skelleftea at the under-18 level and helping and helping Sweden win bronze at the World Under-17 Challenge in 2009. At the 2010 Ivan Hlinka Memorial Cup, Arvidsson tied Ryan Nugent-Hopkins, the No. 1 pick in the 2011 NHL Draft, for the lead in goals (five), helping Sweden to a bronze medal.

In 2011 he had three goals and six points as Skelleftea lost in the Swedish junior league final for the first of two consecutive seasons. He joined Skelleftea's under-18 team for seven 2011 playoff games, ranking fifth among all skaters with 10 points. Arvidsson won silver with Sweden at the 2011 Under-18 World Championship, getting one assist in five games.

Tying for third in the league with 25 goals, Arvidsson was named 2012 Swedish junior player of the year. Moving up to Skelleftea's Swedish Elite League team in 2012-13, Arvidsson ranked fourth among junior players with seven goals, and fifth in points (12). He tied for fourth in goals (six) during the 2013 playoffs as Skelleftea won the title. He also helped Sweden win a silver medal at the 2013 World Junior Championship.

Arvidsson was ninth in the Swedish Hockey League with 40 points in 2013-14. As Skelleftea won its second consecutive league championship, he tied for second in postseason assists (12) and ranked third in points (16). Arvidsson was selected by the Nashville Predators in the fourth round (No. 104) of the 2014 NHL Draft.

He was named to the American Hockey League All-Rookie Team in 2014-15 after leading Milwaukee with 55 points and leading the league with 272 shots. Arvidsson made his NHL debut with Nashville on March 21, 2015, against the Buffalo Sabres and was the only player selected after the first round of the 2014 draft to play in the League in 2014-15.

Arvidsson scored his first NHL goal Oct. 8, 2015, against the Carolina Hurricanes, and got his first Stanley Cup Playoff goal on May 9, 2016, an overtime winner against the San Jose Sharks.