He had previously played in the National Hockey League for the Colorado Avalanche, which drafted him, Montreal Canadiens, Los Angeles Kings, and Tampa Bay Lightning.

Before his first appearance in net, Budaj was diagnosed with the H1N1 virus and was completely isolated from the rest of the team until he was cleared to play by the coaching staff.

[5] Budaj made his second post season appearance on 22 April 2010 against the San Jose Sharks, when he relieved Craig Anderson at 11:05 in the third period.

[7] During the lockout shortened 2012–13 season, his second year as backup to Carey Price, Budaj carried an 8–1–1 record in 13 games, to earn a two-year contract extension with the Canadiens on 10 April 2013.

[12] On 9 October 2015 it was announced that Budaj signed a one-year, two-way contract with the Los Angeles Kings and was subsequently waived and assigned to the Ontario Reign of the AHL to begin the 2015–16 season.

In leading the Reign to claim the Pacific Division title, Budaj led the league in most statistical categories to earn the Baz Bastien Memorial Award as the AHL's best goaltender.

[16] In beating out current backup Jeff Zatkoff, Budaj assumed starting duties for the Kings to cover for the loss of Quick.

[20] While Budaj was originally assigned to the Kings AHL affiliate, after starting goaltender Jonathan Quick was placed on Injured Reserve on 7 October he was recalled to the NHL.

[23] Budaj, a devout Christian, is perhaps best known for having the depiction of Ned Flanders, a popular religious character from TV's The Simpsons painted on his masks.

Budaj's 2009–10 mask features his racing idol Valentino Rossi on one side, the Avalanche's alternate foot logo on the other, and retains Ned Flanders on the back.

He started a goalie training company called Budaj Blockers and also served as assistant coach of the Montana State University Bobcats hockey team.