A resident discovered the baby girl Sunday night.
Police say the box had a slit cut in the lid presumably to allow the baby to breathe.
Nassau County Police medic Timothy Jaccard says he fed the baby and took her to Nassau University Medical Center. He says she's "in very good shape."
The Hempstead building lobby is not a safe haven.
The city's safe haven law allows babies to be left within five days of birth at a police station, firehouse or hospital.
Jaccard is president of the AMT Children of Hope Foundation/Baby Safe Haven Program.
He says the baby is Hispanic and weighs about 5.7 pounds.
She was wearing a "onesie" and was wrapped in a blanket and shirt.