At his bedside hearing, the man was remanded in custody until his first appearance in the High Court at Hamilton.
He is scheduled to appear before a judge on February 4.
Douglas Cres resident Ian, who did not give his surname, said he woke on Wednesday to a police officer outside his house and a pool of blood “dripping into the gutter”.
“It’s a crappy situation,” he said.
“I think it was about 9am and [the police officer] was sitting on a seat and I saw the empty open medic’s bag, and the blood on the ground.
“I thought, ‘Oh, okay, something’s gone down’.”
Ian said it was upsetting to “find out that it’s kids” who had been the victims.
“It’s just all kinds of messed up.“
Hamilton Mayor Paula Southgate said the incident was a tragic start to the year.
“I am hugely saddened by the tragic and senseless death of a child and the harm to others.
“My thoughts are with family, friends and the community of Fairfield,” she said.
Police said emergency services were called shortly after midnight to Douglas Cres after a report of an assault.
“When police arrived at the property, they found one person dead and two others seriously injured, who were transported to hospital.
“A 34-year-old man was found a short distance from the address with serious injuries and was also transported to hospital, where he remains under police guard.”
Detective Inspector Andrew Saunders confirmed later that a baby had died, and another child and a woman remained in hospital in a serious but stable condition.
“We extend our sympathies to the whānau at this tragic time and will provide ongoing support.
“A scene examination is ongoing at the Douglas Cres property, and police are speaking with a number of people as they work to build a full picture of what has occurred.”
Saunders acknowledged it was a “distressing incident”, and the community is understandably concerned.
“We would like to reiterate that this was an isolated event and there is no risk to the wider public.
“Police thank the community for their patience and understanding as we continue to undertake our inquiries.”
The Herald has reported that during the attack the woman ran to get help from neighbours - but the alleged offender “dragged” her back home.
The man was also rushed to hospital with what a source said was self-inflicted injuries.
The last time he saw the injured woman she couldn’t breathe properly but was speaking.
Another neighbour, Kasey, said she and other neighbours helped keep two uninjured children safe, wrapping them in blankets.
“[One child] was playing with a doll and she mimicked what she saw. The trauma that poor child has to live with.”
She said a nana and auntie arrived at the scene and “dropped to ground, screaming and bawling” after learning what had happened.
Anna Leask is a Christchurch-based reporter who covers national crime and justice. She joined the Herald in 2008 and has worked as a journalist for 18 years with a particular focus on family and gender-based violence, child abuse, sexual violence, homicides, mental health and youth crime. She writes, hosts and produces the award-winning podcast A Moment In Crime, released monthly on nzherald.co.nz