They were granted interim name suppression at a court hearing.
Detective Senior Sergeant Neil Holden, officer in charge of the district child protection team, said they are due back in Lower Hutt District Court on the April 16.
"This police case is before the courts and so full details are not able to be disclosed," he said.
John Langley, Child, Youth and Family central regional director, said they were notified of the child's injuries by police.
"We investigated immediately and established there were concerns about the care of this child. She is recovering in the care of wider family."
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