Police revealed that the baby girl from Howick was injured over a period of time, not the result of one incident.
She was taken to a doctor by her family. The doctor then referred the matter to the hospital.
The baby was admitted to Middlemore Hospital on February 18.
Detective Inspector Colin Higson said police had spoken to family members but were no closer to determining who was responsible.
He urged the person who had inflicted the injuries to take responsibility.
Police were making a number of inquiries and confirmed that included interviewing the parents of the child.
However they are still hunting for answers.
"The fractures have been described by medical experts as being of varying ages and classically associated with non-accidental injury," Detective Senior Sergeant Eddie Sutherland told the Herald.
"Thankfully, the child is going to make a full recovery, however police are extremely concerned by these injuries."
Sutherland said the safety and wellbeing of the baby going forward was "paramount" and police had notified The Ministry for Children, Oranga Tamariki.
The baby was now in the agency's custody.
"Police have not yet charged anyone, however our inquiries are ongoing," said Sutherland.
"We are now urging anyone with information which can assist our investigation to do the right thing and contact police."
Oranga Tamariki South Auckland regional manager Jim Wilson confirmed the baby girl was still in the agency's custody and recovering well.
He said the baby was not known to Oranga Tamariki prior to this.
Can you help?
If you have information about how this baby girl was injured - on any occasion - please contact the police.
Information can be passed on to the Counties Manukau Child Protection Team on 09 213 8571, or anonymously through the Crimestoppers reporting line on 0800 555 111.
Members of the public can also send police a private message on Facebook by clicking here.
If you're worried about a child you are urged to contact Oranga Tamariki immediately on 0508 326 459; or email contact@mvcot.govt.nz.
If the child or young person is in immediate danger, call police on 111.