All those who attended the festival should monitor for symptoms and get tested if any symptoms develop, no matter how mild, the ministry said.
No further cases have been linked to the festival and the initial test results of the 11 close contacts of the Wellington case are all negative.
There are 27 new cases in New Zealand today with 35 in hospital and one in ICU.
There are three people in Tauranga Hospital with Covid-19.
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Weekend cases
There were 85 community cases of Covid-19 over the previous two days and 64 cases found at the border during the same period.
The latest community cases are made up 57 people in Auckland, seven in the Waikato region, one person in Taranaki, 16 in Bay of Plenty, two in Lakes and two in Wellington.
The seven-day rolling average of community cases is 30, as of yesterday, and the number of active Covid cases stands at 1087.
Omicron variant
New Zealand has so far managed to dodge a mass Omicron outbreak in the community, but there are serious fears of that happening as the highly transmissable variant has started to become the dominant one at the border.
A total of 500,000 vaccine booster shots have already been administered nationwide, the Ministry of Health announced today.
Australia is seeing an explosion of Omicron cases daily, with Victoria reporting just over 44,000 new Covid cases yesterday.
Epidemiologist Professor Michael Baker says an Omicron outbreak on this side of the Tasman is not a matter of if, but when.
In the past, I would never have said it was inevitable that a new variant would arrive here, but I think Omicron is so infectious that it will be hard to keep it out long-term," Baker told the Herald.
"We have carried out research with Australian colleagues to look at the frequency of border failures.
"In the past, we've had about one border failure per 100 infected people entering MIQ in New Zealand - or an average of one per 167 people across New Zealand and Australia."
Baker said only a minority of those failures triggered significant outbreaks.
But it gave us an idea about how leaks can happen at the border and how risk rises in proportion to the number of infected people arriving in the country.
"Having much more than five to 10 infected travellers per day will result in a high risk of border failure in the next few weeks."