"I am very proud of my daughter Cristina's actions today during an incident in Brooklyn involving a small child," Torre, now Major League Baseball's executive vice president of baseball operations, said in a statement. "Fortunately for that child she was in the right place at the right time to lend a hand."
Cristina Torre did not respond to a request for comment.
Police said a 44-year-old woman caught a 1-year-old boy after he fell from a fire escape outside a Brooklyn apartment building but did not identify the bystander. They said the baby somehow climbed out of the apartment onto the fire escape and tumbled from above. That's when Torre caught the baby as she walked on the sidewalk below.
The baby is in stable condition, police said.
The baby's parents—Sam Miller, 23, and Tiffany Demitro, 24—were arrested and charged with reckless endangerment and acting in a manner injurious to a child less than 17, police said.
The parents were in custody and unavailable for comment Wednesday. It was not immediately known if they had an attorney.
Joe Torre managed the Yankees from 1996 to 2007, winning four World Series titles and six American League pennants. He had a 29-year career as a manager and retired after the 2010 season following three years with the Los Angeles Dodgers.
He played parts of 18 seasons in the majors, with nine All-Star appearances. He was the National League's MVP in 1971, when he led the league with a .363 average for the St. Louis Cardinals.
Torre is also a Brooklyn native.