They should get tested on day 5 and 8 and stay home until all test results come back negative. If symptoms developed they should immediately be tested again.
They should also visit the locations of interest website to record their visit online, or call Healthline.
The Mermaid Club and Femme Fatale were also named on Sunday as sites linked to positive cases in the last two weeks, with the Pelican Club deemed particularly high risk.
Health officials said the club's workers were getting specific advice from their manager.
At the time of the exposure events, Auckland was in the red phase of the traffic light system. In that phase only vaccinated people could do in-person sex work while businesses could only operate if they used the My Vaccine Pass.
Yesterday the Ministry of Health announced just 27 new cases of Covid in the community, with another 24 in managed isolation and quarantine.
The Ministry said the number of positive tests at the border was "a reflection on the increase in cases globally and the continued impact of Covid-19 in many parts of the world".
None of the 24 border cases has yet been identified as the Omicron variant.
So far New Zealand's first community brush with the more-transmissible variant appears to have been a near-miss. All contacts of DJ Dimension - the Omicron-infected musician who was out in the community last week - have tested negative to date.
The UK DJ, real name Robert Etheridge, broke self-isolation rules before receiving his positive test result, but the Ministry of Health says it doesn't intend to refer Etheridge to police.
"The Ministry continues to assess the need for enforcement action in relation to breaches of the Covid-19 Public Health Response Order on a case-by-case basis, and may seek action in instances where this would support the public health response," the Ministry said in a statement.
A police spokeswoman reportedly said any enforcement action over broken isolation rules would come after consultation with the Ministry of Health – and would generally follow a referral from them, which hadn't been received.
Twelve of the new community cases announced on Monday were in Auckland, seven in Waikato, seven in the Bay of Plenty and one in Lakes.
There were 44 people in hospital with an average age of 56. Five were in ICU or a high dependency unit.
The number of unvaccinated people lining up for their first jab has dropped off dramatically, with just 135 first doses on Sunday, 622 second doses and 13 third primary doses. The rest were booster shots.
From Wednesday the number of booster shots is likely to jump as that's the day when the interval between second doses and boosters will drop to four months, with anyone over 18 eligible for a booster.
The Auckland Airport Park and Ride drive-through vaccination centre has reopened to provide for a surge in demand, with the ability to jab more than 4000 arms in a day.
