Further tests have been carried out on both the parent and child.
Police will make inquiries into the incident to see if any further action is required.
Authorities confirmed that the returnee escaped from Middlemore Hospital on Sunday.
A Northern Region Health Coordination Centre spokesperson said the person who had tested negative for Covid-19 on Day 0, was transferred to Middlemore Hospital from a Managed Isolation Facility at midnight.
The patient later left the Emergency Department at around 2am but was not discharged.
Police were notified at 2.25am.
The spokesperson said while the person tested negative for Covid-19 twice since arriving in the country, "it is important that they complete their period of isolation".
The police have been working to locate the person since the weekend.