Police say the woman gave birth to the girl last month in West Islip, then killed her and threw her in the trash.
"Her first story to detectives was that she wasn't pregnant and did not give birth...and she then changed her story and claimed she had delivered the baby on her own but that the baby was born dead," District Attorney Tom Spota said.
But the Medical Examiner determined the infant was born alive and died from "blunt impact injuries of the head."
The baby suffered traumatic injuries and died at the scene, according to police. Prosecutors say she had three fractures to her skull, one of which caused her death.
Officials say the woman then went to a hospital to receive care after the birth, and the baby's remains were found in a plastic bag in a nearby garbage can.
Prosecutors say she had hidden the pregnancy and called her husband afterwards to say she was bleeding and needed help.
She allegedly came to the US illegally from Honduras seven months ago and claims she was raped by her husband's brother in Mexico during the trip. Her attorney says she gave birth to the baby prematurely in a toilet, and the newborn hit her head on porcelain bowl.
Her husband and a friend then became suspicious about the bag and discovered the body.
The woman, who has two other children with her husband, is charged with second-degree murder and has been held without bail since her arrest.