Joint head of MIQ brigadier Rose King said two people fled at 4.45pm on Saturday and police were working alongside MIQ staff to locate them.
"The fact that people have absconded from two of our facilities is a disappointing and unacceptable breach," she said.
King said an investigation was under way into how these events occurred.
Police confirmed they were trying to locate two people who escaped from the Jet Park MIQ facility.
Anyone with information is asked to contact 111 and quote event number P048451440.
In a separate incident, a community case staying at the Novotel & Ibis Ellerslie Managed Isolation Facility allegedly escaped about12.50pm on Saturday, but was located by police shortly after and taken into custody.
The individual is a Covid-19 positive community case who has been in MIQ since October 23.
King said they had no contact with anyone in the community and there was likely to be a low risk to the public because of the short period this person was out of the quarantine facility.
"These facilities are not prisons and these individuals have wilfully absconded. There are rules in place for every single returnee from overseas and now the positive community cases, and we expect people to follow these during their stay in managed isolation or quarantine."
King said "deliberate breaches" put the wider community at risk.
Last month, an infected 23-year-old man escaped from the Novotel MIQ facility
It is understood the man hid in bushes waiting for staff to pass before leaving in the early hours of the morning. He spent 12 hours in the community.
Since this incident, the Ministry of Business Innovation and Employment (MBIE) has increased policing numbers to two and from tonight both stairwells at the facility will have guards posted on the ground floor.
On Sunday 143 new community cases were reported. Of these cases, 135 were in Auckland, six in Waikato and two in Northland. More than half of the new cases are unlinked to existing cases and are under investigation.
These new cases bring the total in the current Delta variant community outbreak to 3348.