Gaudreau spent parts of three seasons with Shawinigan of the Quebec Major Junior Hockey League from 2011-14, which included winning the Memorial Cup championship in 2012, his first season. In 2013-14, he was traded to Drummondville and had 40 of his 71 points that season in 36 games after the trade. Gaudreau took one minor penalty all season and was named the QMJHL's most sportsmanlike player.
After going undrafted, Gaudreau signed with Milwaukee of the American Hockey League on June 12, 2014, and had 11 points (four goals, seven assists) in 43 games. Gaudreau also was loaned to Cincinnati of the ECHL and played 14 games. Milwaukee signed him to a one-year contract for the 2015-16 season. His offensive numbers opened eyes, and the Nashville Predators signed him to a two-year, entry-level contract on Jan. 5, 2016.