It is known whether the cases are linked, but Mr Jones and Mr Needs visited PNG together about 12 days ago.
The trip included a visit to a solar energy project New Zealand helped fund as well as the launch of the Pacific Broadcasting Initiative, under which several New Zealand television programmes will screen free to air in PNG.
Dengue fever is a mosquito-borne viral disease most commonly contracted in countries with tropical and sub-tropical climates.
There has been an increase of cases in the Pacific since 2014. Symptoms include high fever, headaches and joint and muscle pain. It can result in death in a very small amount of cases.
The MFAT travel advisory site Safe Travel cautions travellers to take particular care in Pacific Island countries such as PNG to protect against mosquito bites during the day.
Mr Jones said the doctors at Middlemore had been thorough, including a lumbar puncture to rule out meningitis and tests for zika, dengue fever, typhoid and others.
While the blood tests would not be completed for a week, he was told the symptoms tallied with dengue fever.
"I feel devoid of energy and have extreme pain in the neck and behind the eyes. I feel ridiculous, wearing sunglasses in bed."
He started feeling ill late on Wednesday night and went to the doctor on Friday morning before being sent to hospital.
A spokesman from the Ministry of Foreign Affairs confirmed three of its staff members had suspected dengue fever after working or travelling in PNG recently.
"The staff members have been receiving appropriate medical treatment and we wish them a speedy recovery."
He said MFAT staff posted to PNG or travelling to the region were all advised to take precautions.
There had not been any spike or increase in dengue recently recorded.
