Montoya was drafted with the 6th overall pick by the New York Rangers in the 2004 NHL Entry Draft. On February 26, 2008, the Rangers sent Montoya along with Marcel Hossa to the Phoenix Coyotes for Fredrik Sjöström, David LeNeveu, and Josh Gratton. His first game in the NHL was with the Coyotes on April 1, 2009 and he was able to record a 3-0 shutout victory over the Colorado Avalanche. The Coyotes traded him to the New York Islanders for a sixth round draft pick on February 9, 2011.