Auckland airport staff tested positive for the Covid-19 a day after New Zealand opening a reciprocal travel bubble with Australia.
The lawsuit does not appear to be related to travel bubbles, and flights with Australia have not been suspended.
On Monday, more than a thousand passengers flew for more than a year for the first time in two years.
New Zealand Prime Minister Jacinda Ardern said the victim was clearing planes from “high-risk countries”.
He told reporters that the worker was fully vaccinated, she added that while the jab did not fully eliminate the risk of getting infected, it means positive cases “will not get sick and they will not die.”
Ms. Arden said she had not yet spoken to her Australian counterpart Scott Morrison, but she did not expect the lawsuit to affect travel arrangements between the two countries.
“When we opened the door to both sides, we knew for sure that we would have a case with our border … We acknowledge that it will be part of our journey together, I think Australia has accepted it.”
The long-awaited travel bubble means there is no need for separation when visitors arrive.
According to New Zealand government guidelines for bubbling, travel arrangements will only be closed if a Covid case comes from an unknown source.
If multiple events of an unknown source occur, triggering a regional lockdown in the affected area, the travel bubble will be suspended.
Both New Zealand and Australia have contained the Covid-19 outbreak and have been praised for managing the epidemic.
Strict border controls and snap lockdowns are some of the measures that keep the infection rate low.
Australia recorded 910 and New Zealand 26 deaths.
Both countries closed their borders in March 2020 and introduced quarantine for returning citizens.