Police said the 33-year-old New Jersey woman was posing with her baby in front of the sea lion exhibit and her husband was taking their picture when the branch fell.
The woman and infant were taken to NewYork-Presbyterian/Weill Cornell Medical Center, where the baby was pronounced dead. The mother was listed in stable condition.
Police identified the baby as Gianna Ricciutti of Union City, N.J.
Max Pulsinelli, a spokesman for the Wildlife Conservation Society, which runs the zoo, said he could not comment on the accident beyond what the police had said.
"Our thoughts and prayers are with the family," he said. It's the second fatality caused by a tree branch this year at Central Park.
A 46-year-old man died in February when a branch heavy from snow fell and hit him.
In July 2009, a Google engineer was knocked unconscious after being hit on the head by a rotted tree branch at the park.
