Moncada made his debut for Cienfuegos of the Cuban National Series in 2012. In his two years with Cienfuegos he hit.277/.388/.380 with four home runs and 21 stolen bases. Moncada left Cuba in June 2014 with permission of the Cuban government to pursue a career in Major League Baseball. Before signing with the Red Sox, Moncada was a highly sought after Cuban free agent. He was seen as a generational, five-tool talent, being compared to the likes of Robinson Cano.
Minor leagues
On February 23, 2015, the Boston Red Sox reportedly agreed to terms with Moncada, for a signing bonus of $31.5 million. The contract was finalized on March 12. He made his professional debut with the Greenville Drive of the Class ASouth Atlantic League on May 18. In the winter of 2015, he was consistently cited as one of the top prospects in the Red Sox system. Entering the 2016 season, MLB.com ranked Moncada as the 7th best prospect in Major League Baseball.
On December 6, 2016, the Red Sox traded Moncada, Michael Kopech, Luis Alexander Basabe, and Victor Diaz, to the Chicago White Sox for Chris Sale. Moncada began the 2017 season with the Charlotte Knights of the Class AAAInternational League. On July 19, 2017, he was called up after the trade of Todd Frazier to the New York Yankees. Later that day, he made his Chicago White Sox debut against the Los Angeles Dodgers. He worked a walk in his first at bat, against Kenta Maeda. On July 26, 2017, Moncada hit his first career major league home run off of Jake Arrieta of the Chicago Cubs. On August 25, he was placed on the 10-day disabled list due to shin issues. He played 54 games in 2017, finishing year with a.231 batting average, 8 home runs, and 22 RBIs. In 2018, Moncada played 149 games, finishing with a.235 batting average, 32 doubles, 17 home runs, 61 RBIs, and struck out an MLB-leading 217 times. He had the lowest fielding percentage among major league second basemen, at.963. In the 2019 campaign, Moncada began to play like the former number one prospect he was heralded to be. He set career highs in numerous batting areas, such as hits, doubles, home runs, RBIs, and batting average, among others, with his batting average ranking third in the American League.