The judge, Marilyn Clark, accepted Arroyo's not guilty plea to murder and a weapons charges but ordered a doctor's evaluation to determine whether she is mentally competent to stand trial.
This came after her attorneys said Arroyo's case could rise to the level of not guilty by reason of insanity.
When Clark asked Arroyo if she understood that anything she said could be used against her, Arroyo said, "No."
Arroyo is being held on $750,000 bail at the Passaic County jail.
Police said they were called to the family's home Wednesday night after relatives found the baby, Jose Bell Jr., dead of stab wounds.
Arroyo's attorneys, Gerald M. Saluti and Brooke M. Barnett, said outside of court that she's deeply disturbed.
"We have a very sick young lady, both mentally and physically," Saluti told the Herald News of West Paterson. "We don't even know if she understood who we are. She didn't even know what she did."
Arroyo was living with her mother and the baby in Phoenix, Ariz.
They were visiting relatives in Paterson, including the baby's father.
"She was a good mother. Nobody's denying that," Brenda Lee Melecio, Arroyo's cousin, told the newspaper. "You would least expect this from her. We just want to know why."
If Arroyo can post bail, Clark said a hearing would be held to outline conditions of her release, including whether she would return to Phoenix.
"Quite honestly, living that far out of state I would have issues with," Clark said.
Saluti said it's unknown if Arroyo was suffering from postpartum depression.
"I told her the baby was safe in God's hands," he said. "She had no facial reaction."
