Police said it was believed the individual left the Distinction Hotel for about half an hour, between about 6.30pm and 7pm and went to a liquor store on Te Rapa Road.
He is now in police custody and will appear in court later today.
The man arrived from Sydney on 1 July. He tested negative on his day-3 test and has now had a second test.
Air Commodore Darryn Webb, head of Managed Isolation and Quarantine, said it was "important to note that the Covid-19 health risk has been assessed as very low".
He said authorities were talking to local businesses that may have come into contact with the individual, and were looking at CCTV footage to confirm his movements.
"We have talked to one liquor store on Te Rapa Road where we believe the individual visited, and it has cleaned its premises as a result of our inquiries," Webb said.
"Police ensured no one entered the store this morning until health officials confirmed it was safe to do so."
The store owner has been told it was a "low-risk scenario" and it do not need to close.
CCTV footage at the managed isolation facility has confirmed there were no close contacts and Webb said it appeared there were no close contacts outside the facility.
"As we have said repeatedly - actions such as these are completely unacceptable. Returnees are given clear instructions and information about what their responsibilities are. Managed isolation is a critical part in our defence against Covid-19, and it is up to each and every person entering this country to play their part and abide by the law.
He said 27,723 people had gone through managed isolation since 26 March and the "vast majority" of returnees were taking their responsibilities seriously.
"We take any breach of the Covid-19 rules very seriously. Wilfully leaving our facilities will not be tolerated, and the appropriate action will be taken."
This article is free to read, but it would awesome if we had your support.