They have been placed in the custody of a relative.
Inspector Scott Webb said police went to the house to check on the family after a call from a member of the public.
That person had concerns for the welfare of the mother of the children.
"Police attended and found three children at the address," Webb said.
"Our staff had serious concerns for their welfare and Ministry for Vulnerable Children Oranga Tamariki were called.
"No one has been charged and the woman at the address was taken to hospital for assessment."
Webb could not comment further on the specifics of the incident as police were not the lead agency on the matter.
He referred the Herald to Oranga Tamariki.
Ministry for Vulnerable Children deputy chief executive Glynis Sandland said the agency worked closely with police after they were alerted to the plight of the children.
"We were saddened and shocked at this situation where police attended and identified some young children who needed medical attention and were living within a difficult home situation," she said.
A social worker was dispatched to the hospital within an hour of the agency being alerted and a safety plan was designed for the family.
"The children were medically cleared and we identified a safe whānau member to care for the children," Sandland said.
"After the children were discharged from hospital we followed up to check on their situation within 48 hours, visiting the relative's home, where the children are safe and well.
"We followed up again on 2 and 3 September."
Sandland said Oranga Tamariki would continue to work with the family.
"We are working with the family around longer-term care arrangements for the children supported by our social workers.
"Our goal is to ensure these children are safe and able to thrive in a supportive home environment."
