Montoya was selected by the New York Rangers with the No. 6 pick in the 2004 NHL Draft, but had bad timing: he launched his professional career that year with Hartford of the American Hockey League, just as Henrik Lundqvist was beginning a long run as New York's starting goaltender.

Montoya never played for the Rangers but went on to establish himself as a dependable backup.

The Rangers traded him midway through the 2007-08 season to the then-Phoenix Coyotes, where Ilya Bryzgalov was the starter. Montoya played five games for the Coyotes, all in the 2008-09 season, and spent the bulk of his time playing for San Antonio of the AHL before being traded to the New York Islanders on Feb. 9, 2011.

He spent parts of two seasons with the Islanders, and injuries led to extended playing time. In 2010-2011, he went 9-9-5 in 20 appearances with a .921 save percentage.

On July 4, 2012, Montoya signed with the Winnipeg Jets to back up Ondrej Pavelec. He played in 35 games over two seasons with the Jets and had three shutouts.

In 2014 he signed with the Florida Panthers, where he made 45 appearances over two seasons playing behind Roberto Luongo. On July 1, 2016, Montoya signed with the Montreal Canadiens to once again be a backup, this time to Carey Price.

Born in Chicago, Montoya attended the University of Michigan, where he went 86-29-8 in three seasons. In 2004 he went 6-0 to help lead the United States to its first World Junior Championship title.