He was selected in the first round, sixth overall, by the New York Rangers in the 2004 NHL Entry Draft after a three-year collegiate career with the University of Michigan.

[citation needed] After being signed by the New York Rangers to a three-year entry-level contract in the summer of 2005, Montoya made his professional debut with the Hartford Wolf Pack of the American Hockey League (AHL), the team with which he spent the majority of the next three seasons.

On February 26, 2008, Montoya was traded to the Phoenix Coyotes, along with Marcel Hossa, in exchange for Fredrik Sjöström, David LeNeveu and Josh Gratton.

[7] With Islanders' goaltenders Rick DiPietro and Kevin Poulin sidelined with injuries, Montoya was provided with an opportunity to play regularly in the NHL for the first time.

[citation needed] On July 4, 2012, Montoya was signed by the Winnipeg Jets to back-up starter Ondřej Pavelec on a one-year contract for the 2012–13 season, worth $601,000 after being released by the New York Islanders.

During a November 2016 game against the Columbus Blue Jackets, Montoya allowed 10 goals in a 10–0 Canadiens loss, making it the largest margin of losing by Montreal since December 1995.

[12] On January 4, 2018, the Canadiens traded Montoya to the Edmonton Oilers in exchange for a conditional fourth-round pick in the 2018 NHL Entry Draft.