Child Youth and Family confirmed the couple's three children, all under 10, had been removed.
Last week, Mariam Filihia described Terepo as her son.
"I don't want to share any more information about my son Terepo. He is at rest now. That's all you need to know. "
Detective Inspector Dave Lynch said the Filihias were co-operating with police but explanations of how Terepo was hurt did not account for the severity of the fatal injury.
"The investigation will now focus on reconstructing events over the week period leading up to Terepo being taken to hospital."
Terepo's biological family said there was "huge regret" the couple under investigation were chosen as godparents for the boy, who died just a week after his first birthday.
"These people were there when Terepo's life support was turned off and they were there at the funeral," a close family member said.
"We now know not to judge a book by its cover. We want to know the truth."
Terepo's mother, Terepai Benioni, was called to Middlemore Hospital at 9.30pm on November 4.
"He had tubes everywhere but it was like he was gone: he was already dead," she said.
"We waited till the Sunday and then turned off life support. It was hard."
Police wanted to speak to anyone who had contact with the couple from October 31 to November 4.
If you have information contact Counties Manukau Police on 09 263 2730 or Crimestoppers anonymously on 0800 555 111.
