Márquez signed with the Tampa Bay Rays as an international free agent in July 2011. The Rays added him to their 40-man roster after the 2015 season.  On January 28, 2016, Márquez and Jake McGee were traded to the Colorado Rockies in exchange for Corey Dickerson and Kevin Padlo .  Marquez was promoted to the Major Leagues on September 6, 2016. 
In his first full season in 2017, Márquez went 11-7 with a 4.39 ERA in 162 innings (29 starts), notching a 1.38 WHIP and 147 strikeouts (8.17 K/9). He finished fifth in the National League Rookie of the Year voting.