[1] He pitched for the San Jose Giants of the Class A-Advanced California League in 2013,[2] where he had a 3.31 earned run average (ERA).

The Giants assigned Mejía to the Richmond Flying Squirrels of the Class AA Eastern League in 2014,[3] and he had a 4.67 ERA.

[5] He began the 2016 season with the Sacramento River Cats of the Class AAA Pacific Coast League.

The Twins assigned him to the Rochester Red Wings of the Class AAA International League.

On January 21, 2020, Mejía signed a minor league deal with the Chicago White Sox.

Mejía did not play in a game in 2020 due to the cancellation of the minor league season because of the COVID-19 pandemic.