Police say the woman gave birth to a girl earlier this week in West Islip, then killed her and threw her in the trash.
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 says she was raped by her husband's brother in Mexico during the trip. The defense 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 was ordered held without bail.