He played in Major League Baseball (MLB) for the Los Angeles Dodgers and Houston Astros.

He appeared in two All-Star Futures Games while receiving recognition by Baseball America as having the best infield arm and as the best defensive third baseman in the Dodgers' minor league system.

Báez signed with the Los Angeles Dodgers as a non-drafted free agent out of Bani, Dominican Republic by assistant general manager Logan White on January 22, 2007,[1] and began his career as a third baseman that season with the Gulf Coast Dodgers.

[2] He was again cited by Baseball America as having the best infield arm in the Dodgers system[3] and represented the World team in the 2009 All-Star Futures Game.

[4] In 2010 Báez spent most of the season with the 66ers, but finished the year with the Chattanooga Lookouts of the Class AA Southern League.

[5] Báez appeared in 32 games early in 2011 with the Lookouts, hitting only .210/.278/.381 in 105 at bats before spending most of the season on the disabled list.

After another one game appearance for the Dodgers in July, he joined the bullpen in August and remained there the rest of the season.

[2] He made the roster for the 2014 National League Division Series (NLDS) against the St. Louis Cardinals, and allowed two runs in 2+1⁄3 innings.

[13] The following week Báez was placed on the DL with a right pectoral strain and completed 3 scoreless innings in three rehab appearances in Triple-A Oklahoma City before returning to the big league club.

[23] After receiving written warnings from Commissioner Rob Manfred, Báez decreased his average time between pitches and Jeremy Jeffress took over the distinction of being the slowest relief pitcher in 2017.

[28] Báez missed the beginning of the season after he tested positive for COVID-19 in Spring Training and was placed on the 60-day injured list on April 26, 2021, with shoulder soreness.

He appeared in three games early in the 2022 season for Houston, tallying 2+1⁄3 total innings and allowing five hits, three walks, and three earned runs.

[31] On May 19, 2022, Báez signed a minor league deal to return to the Los Angeles Dodgers organization.

[3] During the 2018 MLB Players Weekend, Báez wore the nickname "LA MULA" ("THE MULE" in Spanish) on his jersey.

Báez says he earned the nickname for his tremendous work ethic in the Los Angeles Dodgers bullpen.