Light was born in Greenville, Ohio. He attended Greenville High School, where he played football as a three-year two-way starter. On defense, he played linebacker and was a second-team Division II all-state selection at the position, and as a senior earned all-county, all-conference, and all-district honors after making 69 tackles and forcing two fumbles. On offense, he played guard as a sophomore, tackle as a junior, and tight end as a senior, when he caught four passes for 75 yards and a touchdown. He also competed in the shot put in track and field, and was a district champion as well as an all-county and all-conference selection.
Light attended Purdue University, where he played for the Purdue Boilermakers football team from 1996 to 1999. He began his career as a true freshman tight end in 1996, appearing in seven games as a reserve and making one reception for 16 yards. He redshirted the 1997 season after undergoing left shoulder surgery in the spring. In 1998, he moved to left tackle, starting 13 games and earning an honorable mention All-Big Ten Conference selection as part of an offensive line that only allowed 16 sacks of future Super Bowl MVPquarterbackDrew Brees. In 1999, Light started 12 games for an offensive line that allowed just 15 sacks, earning second-team All-Big Ten honors. In the 2000 season, Light earned first-team All-Big Ten recognition after starting 12 games at left tackle, helping an offensive line that gave up only seven sacks en route to a Big Ten title and Rose Bowl Game appearance.
Light was drafted in the second round (48th overall) of the 2001 NFL Draft by the New England Patriots. He started 12 of 14 games played during his rookie season in 2001, helping a Patriots running game which averaged 112.2 yards per game. He was the starting left tackle for an offensive line that led the way for 133 yards on 25 carries (5.3 yard average) in the Patriots 20–17 victory in Super Bowl XXXVI over the St. Louis Rams. He was named to the Football News 2001 NFL All-Rookie Team following the season. Light returned in 2002 to start all 16 games at left tackle for the Patriots, who missed the playoffs.
Light began the 2005 season just as he did the previous three, starting at left tackle before a broken leg suffered against the Pittsburgh Steelers in Week 3 kept him inactive for the next 11 games and eventually led to his placement on injured reserve on December 22. He returned in 2006 to start 16 games. He was elected to the 2007 Pro Bowl, replacing the injured Jonathan Ogden, which was Light's first career Pro Bowl appearance.
In the 2008 season, started 16 games for the sixth time in his career. He was ejected from a November 23 game against the Miami Dolphins for fighting with Dolphins linebacker Channing Crowder, who was also ejected. After being named to the Patriots 50th anniversary team in August 2009, Light started the first five games of 2009 before missing five games due to an injury. He returned in Week 12 and started the remainder of the season at left tackle. In 2010, Light started all 16 games at left tackle and was named as an injury replacement to the 2011 Pro Bowl.
On July 31, 2011, Matt Light signed a two-year contract with the New England Patriots.