Of these cases, one was a visitor from French Polynesia with dengue type 3, while the others were dengue type 1.
The ministry said authorities have diagnosed four probable dengue cases this week, one of whom recently arrived from Fiji.
It is reminding the public keep home and work environments clean and to safely dispose of water-retaining containers; to avoid mosquito bites by covering up, using repellents and screen doors, and to see a doctor if fever, pain behind the eyes, or muscle aches develop.
Last week, the Cooks enacted Operation Namu19, a whole of government and community clean-up-our-environment initiative aimed at destroying mosquito breeding and resting sites.
A large number of people participated, including at least 250 public servants.
Over 150 bags of general waste collected contained aluminium cans, tins, glass and plastic bottles.
Other items such as motor vehicle parts, tyres, whiteware and electronics equipment were removed.
In the wake of the dengue outbreak, public health officials will continue to undertake surveillance, awareness raising and closely monitor the situation including spraying of public areas such as schools.
Symptoms of dengue include sudden high fever, severe headaches, pain behind the eyes, muscle and joint pain, as well as nausea, vomiting and sometimes a skin rash.