Director-General of Health Dr Ashley Bloomfield confirmed the latest cases on Tuesday afternoon, and said they were associated with returning from overseas travel.
Two of the cases are in Wellington and one is in Dunedin.
The cases from Wellington are a man in his 30s and his father in his 70s who had been in the United States.
The younger man was unwell on the flight, and his father became ill about a day later.
The man in Dunedin is in his 40s and started showing symptoms after returning from Germany. Two of his family members are also showing symptoms and are in self-isolation.
The man’s son attends Logan Park school and has symptoms. The Ministry of Health is recommending the school closes if he tests positive for the coronavirus.
The three latest cases takes the total number of COVID-19 cases in New Zealand to 11.