Kubel flew home to Phoenix early Wednesday and arrived at the hospital 10 minutes before Heidi Evelyn was born at 11:56 a.m. MST.
The D-backs placed Kubel on the paternity list and recalled outfielder A.J. Pollock to take his spot on the roster. Pollock arrived just before batting practice Wednesday.
Manager Kirk Gibson said that Kubel might rejoin the club as soon as Friday in San Diego, but that by league rules he must be back Saturday.
This is Pollock's second stint in the big leagues this year. He was with the D-backs from April 18 until May 18 while fellow outfielder Chris Young was on the disabled list. In 48 at-bats, Pollock hit .229.
Pollock was headed to the ballpark in Reno, Nev., for a day game when he got the call to come to the big leagues. He was told to make a U-turn, go back to his apartment, pack some clothes and head to San Francisco.
Having already spent a month in the big leagues, Pollock said that getting the callup this time was not as overwhelming as the first time since he now felt comfortable with the guys in the clubhouse and was familiar with the team's routine.
"It's more of a comfortable fired-up," Pollock said. "It's definitely a different feeling. I'm ready for whatever happens."