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, the team with which he spent the majority of the next three seasons. Overall, he posted a 66–34–4 record with the Wolf Pack, along with a 5–5 playoff record. With the emergence of Henrik Lundqvist as an All-Star caliber goaltender, Montoya became expendable to the Rangers. 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. After re-signing with the Coyotes on July 2, 2008, Montoya started the 2008–09 season with the San Antonio Rampage, the Coyotes' AHL affiliate. Later that season, on April 1, 2009, Montoya made his NHL debut with the Coyotes, recording a shutout in a 3–0 victory over the Colorado Avalanche. He went on to appear in five games for the Coyotes in 2008–09, posting a 3–1 record. That spring, Montoya was named to the American roster for the 2009 IIHF World Championship in Switzerland. He started one game at the tournament, a 6–2 win over France. On February 9, 2011, Montoya was traded to the New York Islanders in exchange for a sixth-round draft pick in 2011. 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. He went on to play 21 games for the Islanders, posting a 9–5–5 record with a.921 save percentage and one shutout. On March 29, the Islanders re-signed Montoya to a one-year contract extension. Montoya recorded a 9–11–5 record during the 2011–12 season. Montoya again represented the United States at the 2011 World Championship. He appeared in four games and posted a 2–1 record as the Americans finished a disappointing eighth overall.
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. On July 1, 2014, Montoya was signed as a free agent by the Florida Panthers to a two-year contract with an annual salary of $1.05 million.
On July 1, 2016, Montoya was signed as a free agent by the Montreal Canadiens to a one-year contract with an annual salary of $950,000. He was the backup to starter Carey Price. 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. He kept a positive attitude about the embarrassing loss, saying that the setback only made him stronger. On January 2, 2017, Montoya signed a new two-year contract to last until 2019. 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.
