Rodriguez, 32, was with his wife Cynthia, 34, as she gave birth to the couple's second daughter, born Monday night in Miami, his team announced.
The baby, whose name has not been revealed, weighed 7 lbs., 2 oz., at birth, according to the Major League Baseball Web site.
"We are thrilled with the birth of our second daughter and the blessing of having two beautiful, healthy children in our lives," the happy father said in a statement.
"A new baby girl, so that's exciting," Yankees manager Joe Girardi exclaimed to the Associated Press on Tuesday.
Rodriguez, a two-time American League MVP, and his wife of five and a half years already have a daughter, Natasha, 3. They revealed this second pregnancy exclusively to PEOPLE last October.
"We're thrilled. We can't wait," Cynthia Rodriguez said at the time. "It's almost more exciting [than the first child] in a way, because you can anticipate what you already know is so amazing."
Rodriguez, who had been undergoing treatment on his strained right quadriceps, is expected to rejoin the Yanks on Thursday. At that time, he will be re-evaluated to see when he will again be able to play.
In this season's 20 games so far, Rodriguez is batting .308, with four home runs and 10 RBIs.