The third positive case was linked to the Auckland community outbreak, the Ministry said.
The case involves a household contact of a previous case in the South Auckland cluster, which brings the number of cases in that cluster to 93.
Three cases were still under investigation, including the Rydges maintenance worker, so the total number of cases in the community is 96, the Ministry said.
The number of active cases in New Zealand now stands at 114.
Covid-19 testing by the Lakes District Health Board continues, with 13,702 people tested between January 22 and August 19 this year, with only 0.08 people testing positive.
The number of people tested since August 20 in the Rotorua Lakes area is not yet available.
The number of people in hospital across the country remains at nine.
Two were in Auckland City Hospital, four in Middlemore, two people in North Shore Hospital and one person in Waikato Hospital.
Six people were in a stable condition on a hospital ward, and three people are in an intensive care unit at Middlemore Hospital.
Tomorrow Cabinet ministers will meet to decide whether to change the current alert level settings of level 3 in Auckland and level 2 for the rest of the country.
Those settings are currently in place until 11.59 pm on Wednesday.
Among the factors that will be considered are the number of new cases, whether they can be linked to the South Auckland cluster, and how the contact-tracing system has been performing.
Ministers will also consider the advice of Director-general of Health Dr Ashley Bloomfield.