A teenager accused of trying to take a three-year-old child from her family would be vulnerable in custody and had been diagnosed with schizophrenia, a court has heard.

Police allege Annalise McMillan approached a family at Federation Square on Sunday and picked up the toddler and walked away.

The family was able to get the girl back shortly after, police allege, and Ms McMillan was arrested and charged later that day.

Ms McMillan, 18, of no fixed address, made a brief appearance in Melbourne Magistrates Court on Monday and did not apply for bail.

She is charged with a single count of enticing a child away from the child's parent or guardian.

Defence counsel Jonathan Miller said Ms McMillan had never been in custody before and would be vulnerable in custody due to her age and appearance.

She had been diagnosed with schizophrenia and needed assessment for other mental-health issues, Mr Miller said.

Ms McMillan was remanded in custody to return to court on October 1.