Police said in a statement that they were called, along with ambulance crews, to an Anthony Crescent address in the suburb of Bader about 5.20pm on Sunday.
They had received reports of a "violent altercation".
On arrival, they found a child with critical injuries, who was rushed to hospital.
Police did not give any further details about the child, such as their age.
"Two other adults at the address were also injured - they remain in Waikato Hospital with moderate and serious injuries respectively," the statement said.
"A person of interest has been taken into custody, and police are not currently seeking anyone else."
A scene examination was underway and officers would remain at the property overnight.
Police said they would provide an update on the case on Monday.
