He was admitted with critical head injuries six days earlier.
Staff at the hospital considered the injuries to be non-accidental, and alerted police.
The Herald revealed last week that the baby boy's mother has previously had five other children removed from her care by Oranga Tamariki, formerly called Child, Youth and Family.
Today the mother, who the Herald has chosen not to name at this stage, refused to speak about the baby's death or the police investigation.
"Stay away from me or I will get my lawyer," she said in a message.
"There is no way I am speaking to you.
"I have had legal advice and I will not be speaking to the media."
Police were already investigating how the little boy got his injuries before he died on Saturday.
The investigation was ramped up to a homicide inquiry after he passed away.
At the weekend Detective Senior Sergeant Geoff Baber confirmed a scene examination was underway at an Auckland address, and a post mortem examination would be carried out.
"The death of any child is an absolute tragedy and we are working hard to establish what has caused the child's injuries," Baber said.
"We have previously said that we believe these are non-accidental injuries.
"We are continuing to speak with a number of people in relation to this investigation and have no further updates at this stage."
Oranga Tamariki refuse to be drawn on the little boy's situation, including why he - like his siblings - was not removed from his mother's care, what if any monitoring was in place and whether the agency was investigating the case itself.
OT central Auckland regional manager Anna Palmer said no comment could be made while the police investigation was underway.
"No one wants to see a child seriously injured, or killed," she said.
"We work to improve children's lives and prevent harm."
Palmer also cited "privacy reasons" as to why she could not discuss the child's care or case.
