"Listeriosis usually causes few or no symptoms for most people, but can be serious for pregnant women, newborn babies, seniors, and people with weakened immune systems," the ministry said.
Te Marae Ora is working closely with Auckland Regional Public Health Service to investigate the case.
It says listeria is likely to be found in foods such as unpasteurised milk and cheese, as well as some seafood and processed meats such as luncheon meat and salami.
Health officials are looking out for patients who might present with symptoms of listeriosis such as fever, chills, muscle aches, nausea and diarrhoea.
Apii Te Uki Ou principal Mark Harris and board president Tony Fe'ao wrote to families last night.
"Our hearts, thoughts and prayers go out to Grace, Theo and their families at this very difficult time," they said. "Please keep them both in your thoughts and we are all very hopeful Grace will make a full recovery and return to us, as soon as possible."
Archer, taught the year 3 and 4 Kukupa class, but had recently been experiencing issues with her health, they said. After nearly three weeks of medical treatment, testing and support here on Rarotonga, doctors referred her to New Zealand for more tests – but her condition deteriorated rapidly.
"This is an extremely difficult time for our school and community," Harris and Fe'ao said.
"In their short time at our school, both of these wonderful team members have shown exceptional commitment to our school and students, bring a vibrant energy to what they do, are very impressive teachers and are beautiful people in every way."
The school says it will advise families how they can offer financial support to Archer and Warrick.
According to the World Health Organization, listeriosis is a serious and severe foodborne disease, but it is preventable and treatable.
Pregnant women, the elderly or individuals with a weakened immune system are at greatest risk of severe listeriosis.
New-born babies who develop listeriosis can have difficulty breathing, develop a chest infection, and inflammation of the coverings of the brain (meningitis). This can sometimes cause death.
- Cook Island News