"We are thrilled with the birth of our second daughter and the blessing of having two beautiful, healthy children in our lives," Rodriguez said in a statement.
A-Rod, who also has a 3-year-old daughter, Natasha, will not be in the Yankees lineup Tuesday or Wednesday as he spends time with his expanded family.
He is expected to rejoin the team Thursday in Chicago, though Yankees manager Joe Girardi is not certain if Rodriguez would be able to play. The reigning American League MVP is treating a strained right quadriceps, suffered on Sunday in Baltimore while running out a fielder's choice.
Girardi said he spoke to Rodriguez via telephone Tuesday.
"He was good," Girardi said. "He was excited about his baby. He's going to get treatment today and Alex is such a great conditioned athlete that hopefully that pays off in a situation like this. Maybe he responds quicker to treatment than a normal human being."
Rodriguez is batting .308 with four home runs and 10 RBIs in 20 games this season. Morgan Ensberg was in the Yankees lineup on Tuesday at U.S. Cellular Field playing third base.
"We'll see how the treatments go and how [Rodriguez] responds to it," Girardi said. "The one thing you can't do is rush him and lose him for a long period of time."
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.