Alexis Avila, 18, appeared in court on Wednesday and entered her plea. She was afterwards released under house arrest while awaiting trial.
The resident of Hobbs, a town roughly 260 miles southwest of Albuquerque, reportedly told investigators that she had abandoned her newborn baby.
She was arrested last week after her car appeared in a surveillance video on 7 January throwing a trash bag into a dumpster outside a shopping mall in Hobbs.
“We just found a baby in the god***n trash,” a member of the public could be heard telling 911 dispatchers on 7 January, in audio obtained by obtained by KQRE.
“He’s whimpering, he was not crying actually. I was looking for some stuff in the dumpster and we heard ... We heard something I didn’t know it was a baby. Thought it was a cat,” the caller added.
Authorities said Ms Avila had not realised she was pregnant until 6 January, when she began to experience pains and birthed the child shortly after.
Search warrants for her car and family home meanwhile resulted in police locating blood evidence, clothing and a towel.
The baby has been put into the hands of the New Mexico Department of Children, Youth and Families, who are caring for the infant.
Additional reporting by The Associated Press.