Torrealba will fly to be with his wife in the Miami area, but he is expected to return to the team next weekend when it visits the Los Angeles Angels in Anaheim, Calif.
In the meantime, the Rangers could use the paternity leave list to fill Torrealba's roster spot for up to three days.
Torrealba was in the starting lineup for Sunday's game against the Seattle Mariners.
Rangers manager Ron Washington expects catcher Mike Napoli to be available for the series opener against the Athletics on Tuesday. Napoli left Friday's win against the Mariners with a bruised right quad muscle just above his knee. He did not play in Saturday's loss, and the Rangers recalled catcher Luis Martinez from Triple-A Round Rock. Napoli was also out of Sunday's starting lineup.
"He showed me (Saturday) that if I needed him in an emergency he could go," Washington said of Napoli.
Martinez will serve as the backup catcher during Torrealba's absence unless Napoli is unable to go Tuesday.
Napoli said the injury feels much better but remains sore.
"It's not exactly how I wanted to start the second half," Napoli said.
In his first season with the Rangers last year, Napoli had a remarkable second half. After hitting .232 with a .529 slugging percentage in the first half, Napoli turned it around after the All-Star break, hitting .383 batting with a .706 slugging percentage. Napoli collected 18 of his 30 home runs and 42 of his 75 RBIs after the 2011 All-Star break.
Master Tesfatsion is a contributor to ESPNDallas.com.