Monroe attended Helen Cox High School in Harvey, Louisiana. As a senior in 2007–08, he was named a McDonald's All-American and earned Parade All-America first team honors after averaging 21.0 points and 14.0 rebounds per game.
Considered a five-star recruit by Rivals.com, Monroe was listed as the No. 1 power forward and the No. 8 player in the nation in 2008.
In his freshman season at Georgetown, Monroe was named the Big East Rookie of the Year and earned Big East All-Rookie team and CBSSports.com NCAA Freshman All-American first team honors. In 31 games, he averaged 12.7 points, 6.5 rebounds, 2.5 assists, 1.8 steals, and 1.5 blocks in 30.9 minutes per game.
In his sophomore season, Monroe was named to the All-Big East first team, Big East All-Tournament team, USBWA All-District II team, NABC Division I All-District 5 first team, AP NCAA All-America third team and NABC Division I All-America third team. In 34 games, he averaged 16.1 points, 9.6 rebounds, 3.8 assists, 1.2 steals and 1.5 blocks in 34.2 minutes per game.
On April 17, 2010, Monroe declared for the NBA draft, foregoing his final two years of college eligibility.
Monroe was selected with the 7th overall pick in the 2010 NBA draft by the Detroit Pistons. On July 6, 2010, he signed with the Pistons.
Monroe made his NBA regular season debut on October 30, 2010 against the Chicago Bulls. He came off the bench to score 2 points and 3 rebounds in 7 minutes. After coming off the bench for the first month of the season, Monroe made his first career start on December 10, 2010 against the Minnesota Timberwolves. In this game, Monroe recorded eight points, fifteen rebounds, and a block in 35 minutes of action. Despite a slow start to the season, Monroe's production increased in 2011 as he became a solid scorer and rebounder for the rebuilding Pistons. On February 23, 2011, against the Indiana Pacers, Monroe had his best game of the season with 27 points and 12 rebounds on 11–17 shooting.
On May 4, 2011, Monroe placed sixth in NBA Rookie of the Year voting totals, finishing closely behind Gary Neal of San Antonio.
During the 2011–12 season, Monroe played in and started all of Detroit's 66 games. On February 8, 2012, he was selected to play in the NBA All-Star Weekend Rising Stars Challenge. Monroe and teammate Brandon Knight were both selected for Team Shaq, despite them being drafted in different years.
During the 2013–14 season, Monroe recorded his third consecutive season with 1,000-plus points and 600-plus rebounds, joining Grant Hill as the only Pistons to do so since 1994–95.
On June 30, 2014, the Pistons tendered a one-year qualifying offer to make Monroe a restricted free agent. On September 8, 2014, it was announced Monroe signed the Pistons' qualifying offer, thus making him an unrestricted free agent in 2015. The next day, the NBA suspended Monroe without pay for the first two games of the 2014–15 season for driving while visibly impaired in February 2014. On December 3, 2014, he scored a season-high 29 points in a 102–109 overtime loss to the Boston Celtics. On April 8, 2015, he returned to action after missing 11 games with a knee injury to record 19 points and 10 rebounds in another loss to the Celtics.
On July 9, 2015, Monroe signed a three-year, $50 million contract with the Milwaukee Bucks. He made his debut for the Bucks in their season opener on October 28, 2015, recording 22 points and 14 rebounds in a 122–97 loss to the New York Knicks. Between February 9 and March 7, 2016, Monroe had a 12-game bench stint as head coach Jason Kidd tinkered with his line-up. In his first game coming off the bench, he recorded a season-high 29 points and 12 rebounds in a 112–111 win over the Boston Celtics. Monroe returned to the starting line-up on March 9 for the Bucks' game against the Miami Heat.
Monroe was assigned a permanent bench role for the Bucks in 2016–17 by coach Kidd. On January 25, 2017, he led the Bucks with a season-high 28 points in a 114–109 loss to the Philadelphia 76ers.