Munson attended USC with former Astros teammates Jason Lane and Morgan Ensberg. He graduated from San Diego's Mount Carmel High School where he played baseball with Oakland Athletics third baseman Eric Chavez.

Munson was first drafted out of high school in 1996 by the Atlanta Braves, who chose him 62nd overall in the 2nd round. Munson however did not sign, opting to play college baseball at the University of Southern California, where he was named Freshman All-American. After three seasons at USC, Munson was drafted third overall in the 1st round of the 1999 amateur draft by the Detroit Tigers. The Tigers were able to sign Munson with a $3.50 million signing bonus, a team record until Rick Porcello was signed for $3.58 million in 2007. Despite playing the catcher position in high school and college, the Tigers had drafted Munson mostly for his hitting skills, and the decision was made to shift him to first base. Although his batting average was merely average (.260s), Munson hit for power in the minor leagues, and was named to the Midwest League All Star Team in 1999 and the Eastern League All Star Team in 2001. In 2002, while playing for the Toledo Mud Hens, Munson was named the Detroit Tigers Minor League Player of the Year.

Munson began his major league career with the Detroit Tigers, making his first appearances in three games during a September call-up in 2000. He also made September appearances in 2001 and 2002. During spring training prior to the 2003 season, Munson was asked to try the third base position, as the Tigers had previously acquired Carlos Pena and Dmitri Young, both of whom were slated to play first base or designated hitter. The club's regular third baseman, Dean Palmer, was dealing with numerous injuries and would not be available. After strong play during spring training, Tigers official, Brad Lockwood, declared Munson to be the Tigers #1 prospect, and a sure fire future Gold Glover. Munson would go on to play in 91 games at third and commit 19 errors for a .920 fielding percentage, eventually losing playing time to utilityman Shane Halter. On June 26, 2004, he hit the longest home run in the history of Comerica Park off Arizona Diamondbacks pitcher Brandon Villafuerte. The ball traveled an estimated 457 feet over the center field fence. During the same year, Brandon Inge began to play third base, among other positions, and the Tigers chose to grant Munson free agency. He signed with the Minnesota Twins in early 2005, but was released during spring training. Munson soon thereafter signed with the Tampa Bay Devil Rays' top affiliate, the Durham Bulls, where he again played first base. Munson also appeared in 11 games for the Devil Rays.

Prior to the 2006 season, Munson was signed as a minor league free agent by the Houston Astros. With Houston, he has backed up Brad Ausmus at catcher, the position he played in college at USC. On August 20, 2006, Munson was designated for assignment by the Astros and he accepted a demotion to their Triple-A affiliate, the Round Rock Express, in the Pacific Coast League. He returned to Houston when the major league rosters expanded in September. Munson again signed a minor league contract with the Express for 2007, and began the season in the minors. Due to the injury to Astros catcher Héctor Giménez, Munson was recalled to the major league roster on June 2, 2007.

Munson was claimed off waivers by the Brewers on October 15, 2007. On March 26, he was sent outright to the Brewers' Triple-A club in Nashville. There, he split his time between first base and catcher. He became a free agent at the end of the season.

Munson signed a minor league deal with the Oakland Athletics on March 27, 2009 and has reported to the Athletics' Triple-A affiliate, the Sacramento River Cats. On September 11, 2009, Munson's contract was purchased from triple-A and he joined the A's as a September call-up. In October 2009 Munson Was Granted Free Agency.

On February 25, 2010, Munson signed a minor league contract with the San Diego Padres.

On July 6, 2010, Portland Beavers released Munson.