The Health Ministry says the latest patient is a 64 year-old woman who arrived on a repatriation flight from India on 27 August.
Last week, the ministry announced two men who were on the same flight had tested positive to the virus.
It said more than 200 passengers were onboard that flight and they had travelled from Delhi via Fiji, landing in Christchurch late on 27 August.
New Zealand's Health Ministry also announced last week that five passengers on the same flight tested positive after arriving in Christchurch.
The New Zealand ministry said the five new cases had stayed at an isolation hotel in New Delhi for three days before their flight - and were all tested before being allowed on the plane.
Fiji's acting Health Secretary James Fong said there was no threat to the public as the Christchurch-bound passengers did not leave the terminal in Nadi.
Dr Fong confirmed on Wednesday the woman is the 12th person to contract the virus while in quarantine.
He said she is in a stable condition in isolation at Lautoka Hospital.
Dr Fong said the frontline border staff involved with the passengers on this flight had also been tested and they all returned negative results.
Fiji now has six active cases, all in border quarantine.