LSG Sky Chefs say all staff - except the original case - who work at the Auckland business have returned negative test results for Covid-19.
A woman who works at the laundry was one of the three community cases reported at the weekend.
In a statement, the German company says no other employee has been infected and it will resume supplying customers tomorrow.
All of the company's 270 employees have been tested.
The woman who tested positive is one of eight working in the laundry department. They have no access to the airport, no face-to-face contact with crews or passengers and do not handle international crew uniforms.
They wash and iron linen, napkins, blankets and sheets from international flights.
An on-site audit declared the infection control processes already implemented were safe, the company said.
The negative test results reflect the fact that the safety and hygiene processes we have in place at the unit are effective, benefiting both our employees and customers, general manager Mauricio Novaes said.
"Of course, we always want to improve and, therefore, plan to introduce the government's testing software within the next two weeks. In addition, we were informed today that our workforce would be vaccinated very soon."
The source of the current Covid-19 outbreak has not been identified.