Díaz began his career with the Naranjas de Villa Clara in the 2008-09 Cuban National Series; at 16 years old, he registered two hits and two walks over seven plate appearances. The next year with Villa Clara, he slashed .292/.417/.351 in 67 games. In his final season with Villa Clara, he slashed .254/.399/.331 in 59 games. He was not included on the roster for the 2012–13 season, which saw Villa Clara win the championship.
In 2013, at 21 years old, Diaz defected from Holguin, Cuba to Monte Cristi, Dominican Republic alongside his childhood friend Leandro Linares and another unnamed individual.[1] He had previously attempted to defect twice, both times which he was caught and arrested by the Cuban government. In August, he signed with the Cleveland Indians for $300,000.[2]
Díaz earned a non-roster invitation to the Indians' 2017 major league spring training camp. After batting .458 (22-for-48) with a 1.252 OPS during spring training, and after injuries to other players forced the Indians to adjust their roster, Díaz was named the Indians' starting third baseman for the start of the 2017 season.[8][9] Diaz played 49 games, slashing .262/.352/.327 predominantly playing third base.
Diaz spent the 2018 season between Columbus and the Cleveland Indians, playing 39 games and slashing .312/.375/.422 with one home run and 15 RBIs.
Tampa Bay Rays
On December 13, 2018, the Indians traded Díaz to the Tampa Bay Rays in a three-team trade in which the Rays also acquired Cole Sulser for Jake Bauers, and the Seattle Mariners acquired Edwin Encarnación from the Indians for Carlos Santana.[10] Díaz missed some time due to injury during the season, only accumulating 307 at bats. He did hit 14 home runs and 38 RBI.
Although plagued by a hamstring injury in September 2020, Díaz appeared in 34 games of the abbreviated 2020 season, slashing .307/.428/.386 with 2 home runs and 11 RBI.[12]
In the 2022 season, Díaz hit .296/.401/.423, leading the Rays in on-base percentage (.401), OPS (.824), and OPS+ (142), and finished second only to Harold Ramírez in batting average. He received MVP votes for the first time in his career. On January 31, 2023, he signed a three–year, $24 million contract extension with the Rays.[13]
Díaz was named to his first All-Star Game in 2023, when he was elected the American League starter at first base. In his first at-bat, he hit a solo home run to put the AL up 1-0, becoming the first Rays starter to homer in an All-Star Game and the first Cuban-born player to do so since Cookie Rojas in 1972.[14] Notably, Diaz and his wife welcomed their first son the day after the All-Star Game, meaning that Diaz flew into Seattle the morning of the All-Star Game and flew back immediately after. He was officially placed on the paternity list on July 14.[15] Díaz led the AL in batting average (beating out Corey Seager on the last day of the season) and in batting average on balls in play (.367), as he hit .330/.410/.522 with 22 home runs and 78 runs batted in.[16] In doing so, he became the third Cuban-born player to win a batting title, after Tony Oliva and Yuli Gurriel. Díaz also won the 2023 Silver Slugger Award for AL first basemen.[17]
In 2024 Díaz had a 20-game hitting streak, breaking Jason Bartlett's record for the longest streak in Rays history.
His father, Jorge, also defected from Cuba to play professional baseball in the United States. Jorge Díaz briefly played in the Texas Rangers organization and spent the rest of his career in independent leagues.[19] Yandy was six years old when he last saw his father.[20] Diaz is of Afro-Cuban descent.
Díaz is married to his wife, Mayisleidis. They welcomed a son, Yandy Jared Díaz, in July 2023.[15][21]