Players are allowed to miss a maximum of three games under paternity leave. The Rangers purchased the contract of infielder Luis Hernandez from Triple-A Round Rock to take Young's spot on the roster.
Young, the designated hitter in Thursday's game with the Minnesota Twins, left the ballpark in the fifth inning to be with his wife, Cristina Barbosa, who gave birth to a boy around 9 p.m. Thursday.
The Rangers report that mother and son are doing fine.
Mitch Moreland was in the on-deck circle to bat for Young as the fifth inning ended.
Young originally was in the lineup as the shortstop, but things were changed about an hour before the game with Elvis Andrus going in at short and Young as the DH just in case he had to leave. Young was 0 for 1 with a walk before exiting the game.
Young and his wife now have three sons, along with Mateo (7 years old) and Emilio (2).