Murton was drafted out of Georgia Tech baseball in the supplemental first round of the 2003 MLB draft by the Boston Red Sox. Murton played a total of 155 games in the Red Sox organization for the Lowell Spinners and the Sarasota Red Sox.
Murton was acquired at the 2004 trading deadline by the Chicago Cubs along with Red Sox star shortstop and fellow former Georgia Tech Yellow Jacket Nomar Garciaparra as part of a four-team blockbuster deal. He spent the rest of the year with the Class A-Advanced Daytona Cubs.
He started 2005 with the Double-A West Tenn Diamond Jaxx, but was called up to the major leagues for the first time on July 8, along with Adam Greenberg, to replace the struggling Corey Patterson and Jason Dubois. On the same day, he went 2-for-2 with a walk and a sacrifice fly against the Florida Marlins in his major league debut. He continued his success in the majors over the rest of the season, hitting .321 with two stolen bases, seven home runs, and an on-base percentage of .386 in 51 games in 2005.
In 2006, Murton became the Cubs' starting left fielder. On August 3, 2006, Murton went 4-for-4 with 4 doubles and 5 RBIs in game 2 of a doubleheader against the Arizona Diamondbacks, matching a major league record for doubles in a single game. He finished the year with the second-highest mark on the team in batting average, at .297, with 13 home runs and 62 runs batted in.
For 2007, Murton saw his playing time reduced when the Cubs signed Cliff Floyd to play in left field. When center fielder Alfonso Soriano switched back to left field in April, Murton switched to right field. On June 13, after hitting only one home run with eight RBIs in limited playing time, Murton was optioned to Triple-A to make room for left-handed pitcher Clay Rapada.
On July 27, 2007, Murton was called back up to the major leagues, along with pitcher Rocky Cherry, with his first start coming on July 30.
In 2008, Murton saw his playing time diminish even further, playing in just nineteen games, and recording only 42 plate appearances in the first three months of the season for the Cubs. In those 42 plate appearances, he managed only two hits, and spent most of the first half of the season in the minors.
On July 8, 2008, Murton was traded along with Cubs prospects Josh Donaldson, Eric Patterson, and Sean Gallagher to the Oakland Athletics for pitchers Rich Harden and Chad Gaudin.
On February 4, 2009, Murton was traded to the Colorado Rockies for infielder Corey Wimberly. When stepping to the plate at Rockies home games, the song "Strong Tower" by Kutless was played over the speaker system.
On December 4, 2009, Murton was released by the Rockies, who sold his contract to the Hanshin Tigers of Japan's Nippon Professional Baseball.
In Murton's rookie season with the Hanshin Tigers he became only the fourth player in Nippon Professional Baseball history to have a 200-hit season. On October 5, 2010, Murton broke the NPB single- season hit record of 210, set by Ichiro Suzuki in 1994 (in 130 games), getting his 211th hit in game #142. He finished his first season in Japan with 214 hits, a .349 batting average, 17 home runs and 91 RBIs.
Murton's single-season hits record was eclipsed in 2015 by Shogo Akiyama of the Seibu Lions, who recorded 216 hits in 143 games.
Murton played six seasons for the Hanshin Tigers, with a .310 career batting average and 1,020 hits. In 2015, Murton became the 16th foreign player to achieve 1,000 career hits in NPB.
On February 16, 2016, Murton returned to MLB and signed a minor league contract with the Chicago Cubs. After 76 games with the minor league Iowa Cubs, Murton was released on November 7, 2016.
On February, 20, 2017, Murton signed a minor league contract with the Detroit Tigers. The Tigers released him on April 18, 2017.
Murton is married to Stephanie Murton and has homes in Georgia, Florida, and Colorado. Murton played baseball for Eagles Landing High School in McDonough, Georgia, and later for the Georgia Tech Yellow Jackets. Matt's younger brother, Luke, also played for Georgia Tech and is currently in the New York Yankees farm system. It is rumored that Matt will occasionally attend Hanshin Tigers games and sit in the grand stands incognito.