Edwards appeared solemn in the dock in a blue sweatshirt.
Ten supporters waved and shouted to him from the public gallery.
An older woman yelled: "Love you my bubby" as he was led away.
Edwards was remanded in custody without plea until February 5 when he will reappear in the High Court at Hamilton.
The baby boy remained in intensive care at Waikato Hospital.
Family members have posted on Facebook about Hurinui's death - one woman sharing a link to a story about the incident along with the words, "How can this be? R.I.P my cousin".
Another woman commenting on the thread wrote: "I still can't believe you're gone sis".
"Taken way too soon. Love also to your baby as well. Get well little one. RIP my girl".
"Me n our 6 kids will never forget you mish. We love you for life," another man wrote.
The incident has rocked the Matamata community - Matamata Piako District Council Mayor Jan Barnes labelling it "very, very sad".
"So tragic, there is no winners in any of this," Barnes said.
Waikato police Detective Senior Sergeant Stephen Ambler said emergency services were called to a Matamata property at 1pm on Monday.
The baby was airlifted to Waikato Hospital. A spokeswoman from the hospital confirmed yesterday morning they remained in critical condition in the Intensive Care Unit.
It is understood the property was rented.
Jamie Kennedy, a farm manager of a neighbouring property, said he just had arrived back to find emergency services had cordoned off the property.
There were three different houses down the next door driveway, he said.
"I just came back from golf and thought, 'What the hell's going on down there'."
He had no details about the tragedy that had occurred.
A woman posted on Facebook: "Heard the sirens before. Very sad, sending my love to the women [sic] who has passed and that poor little baby xxx."
Another neighbour believed a brother and sister lived at the property.
"We have seen her pushing a pushchair with the baby in it down the driveway," they told Stuff.
"They haven't been living there very long a couple of months."
The Herald understands the rescue helicopter responded to a house on State Highway 27, Matamata.