An MIQ spokesman said there have been five incidents involving 10 people between Dec 12 last year and Feb 9.
Ten people have been referred to the police for attempting to enter New Zealand without an MIQ voucher.
These people arrive as transit passengers without vouchers, and then refused to board their onward flights.
"Police are aware of a small number of reports of this nature and are making ongoing inquiries," a police spokesman said.
An MIQ spokesman said there have been five incidents involving 10 people between December 12 last year and February 9.
"All have been referred to police," the spokesman said.
"MBIE and MIQ are not an enforcement agency. It is a legal requirement to have a valid MIQ voucher on arrival in New Zealand, so we provide the details to NZ Police but any further action is at their discretion."
Last November, the Herald revealed altered MIQ vouchers were used by desperate travellers to dodge the MIQ lottery.
One who made simple alterations got him back to NZ and straight into a Rotorua quarantine slot with no questions asked.
Another said he was driven by desperation, altered an out-dated MIQ voucher and got into two weeks MIQ at the Four Points Sheraton Hotel in Auckland.
That traveller was fined $300 - but the maximum penalty now stands at $4000 after a law change last November.
The Auckland man said he was sharing his story with the Herald to highlight the plight of those trapped overseas and unable to get home.
"What could possibly stand in the way of a New Zealander trying to get home to his country and his family," he said at the time.
When he arrived at the airport, the man checked in and showed the altered letter when boarding the plane.
"The name, passport number and flight number were all the same. The guy (at the aircraft) scanned it and gave it just a cursory glance," he said.
When he arrived and produced a negative Covid test and passport, he said he was told that he wasn't on the list.
However, the person checking him in handed him a room card, assured him his details would be added manually and that the Ministry of Health would be told.
In the Rotorua case, NZDF MIQ co-manager Brigadier Rose King said what the person did was illegal.
She said the person arrived on October 29 and it was found on arrival that they did not have a valid MIQ voucher.
"As citizens cannot be deported, they were taken to an MIQ facility in Rotorua where they spent their isolation period."
The person left MIQ on November 11 after being issued a $300 fine by police.
'He has disregarded our voice and continued with this divisive kaupapa.'