The MIQ official said there was an extremely high threshold for approving applications and the majority were declined.
"This is because as a key factor in assessing any application is the public health risk of transmitting Covid-19 to the community.
"If applicants are considered too high risk for spreading Covid-19, or it is deemed that the risk cannot be appropriately managed, the application will be declined."
The MIQ official did not respond to a request for the reasons for approving the applications.
All applications were assessed on a case-by-case basis, the spokesperson said.
Otago University Professor of public health Nick Wilson said there could be reasonable explanations for this, such as someone being claustrophobic or needing access to complex equipment such as a dialysis machine.
"If people were allowed to isolate at home then it should be done extremely carefully, with digital tracking and major fines if there were any breaches."
He said New Zealand should not loosen its criteria to allow more people to isolate at home, especially given the heightened risk from the second strain of Covid-19.
Otago University epidemiologist Professor Michael Baker said given thousands of travellers had entered New Zealand in the past six months, six people was a very tiny number.
"Every health system was going to come with exemptions. We need strong rules, there is no question about that, but occasionally there will be circumstances where you have to change things."
He said at the moment we should be trying very hard to avoid allowing people to isolate at home because of the much higher risk of spread carried by the second strain from the UK.
It comes after 18 new cases of Covid were reported in the past two days - all in managed isolation.
One case from South Africa tested positive on day 18, said the Ministry of Health in a statement. That person was in a travel bubble of a previously confirmed case reported on December 31.
The traveller arrived from South Africa via the United Arab Emirates on December 26 and has been in Auckland's Jet Park quarantine facility since the contact case was first detected.
The other cases come from all over the world including the US, Malaysia, India, South Africa, Italy, United Kingdom, Russia, Bahrain, and the United Arab Emirates.
Meanwhile, people from the Cook Islands will be allowed to come to New Zealand without going into quarantine from next week. The new arrangements do not apply to New Zealanders wishing to travel to the Cook Islands.
"We said we would take a phased approach to resuming two-way travel and will do so only once all safety protocols can be met," Prime Minister Jacinda Ardern said.
The new arrangements will allow specialist workers and contractors and the judiciary to come to Rarotonga for short terms without the need for two-week quarantine on return.
"Following confirmation of the Cook Islands' Covid-free status, and the implementation of strict health and border protocols we are now in the position to resume quarantine-free travel for passengers from the Cook Islands into New Zealand," Ardern said.
Cook Islands Prime Minister Mark Brown said Cook Islanders needed to access essential services here.
Strict protocols would be in place including pre-departure health requirements and separation from other travellers at Auckland International Airport, to prevent the risk of Covid spread from travellers from other countries, Ardern said.