He did not sign with Cleveland and attended Baylor University. He played college baseball for the Baylor Bears from 2010 to 2012, and also played collegiate summer baseball for the Wareham Gatemen of the Cape Cod Baseball League in 2010 and 2011. In his three years at Baylor, Muncy had a .311 batting average with 27 home runs. He was twice chosen to the All-Big 12 Conference team.

The Oakland Athletics selected Muncy in the fifth round of the 2012 Major League Baseball draft. He made his professional debut with the Burlington Bees of the Class A Midwest League, hitting .275/.383/.432 with four home runs in 64 games. He started the 2013 season with the Stockton Ports of the Class A-Advanced California League before being promoted to the Midland RockHounds of the Class AA Texas League. At the time of his promotion he was leading the California League with 21 home runs and 76 runs batted in (RBIs). In total, Muncy hit .273/.381/.476 with 25 home runs and 100 RBIs. After the season, he played for the Mesa Solar Sox of the Arizona Fall League. He returned to Midland in 2014.

Muncy began the 2015 season with the Nashville Sounds of the Class AAA Pacific Coast League (PCL), but was promoted to the major leagues on April 25 after second baseman Ben Zobrist was placed on the 15-day disabled list. On May 17, 2015, Muncy hit his first major league home run off of Chicago White Sox pitcher Jeff Samardzija. He batted .206 in 45 games for Oakland in 2015. He split the 2016 season between Nashville and Oakland, batting .186 in 51 major league games in 2016. The Athletics released Muncy towards the end of spring training in 2017.

Muncy signed a minor league contract with the Los Angeles Dodgers on April 27, 2017, and the organization assigned him to the Oklahoma City Dodgers of the PCL. In 109 games, he hit .309 with 12 homers and 44 RBIs.

Muncy was called up to the Dodgers on April 17, 2018. He hit his 20th home run for the Dodgers in his 183rd at bat, setting a franchise record. Muncy was chosen as a candidate for the All-Star Final Vote for the 2018 MLB All-Star Game, but he finished in third place in the voting. He also accepted an offer to participate in the Home Run Derby during the All-Star break. After beating Javier Báez in the first round of the Derby, he lost to eventual champion Bryce Harper in the semi-finals.

In 2019, Muncy was selected to the 2019 Major League Baseball All-Star Game as an injury replacement, his first all-star appearance, replacing Washington Nationals third baseman Anthony Rendon. On August 30, 2019, Muncy was placed on injured list with a wrist fracture. He finished the 2019 regular season, playing in 142 games, hitting .251/.374/.515 with 35 home runs (for the second season in a row) and a career-high 98 RBIs. Muncy also received two MVP votes.

On February 6, 2020, the Dodgers and Muncy agreed to a three-year, $26 million contract extension with a $13 million option for a fourth year. The 2020 season was delayed due to the COVID-19 pandemic in North America. Muncy played in 58 of the Dodgers’ 60 games and hit .192/.331/.389 with 12 homers and 27 RBIs. In the 2020 World Series, he batted .318 with one home run and six RBIs and helped the Dodgers win the championship.