The pair are currently isolating and being supported on the Island.
Skinner said the DHB would be distributing RAT tests to all households on the Islands early this week to allow for early case detection.
"We encourage anyone who has symptoms to have a RAT test and report their results to My Covid Record mycovidrecord.health.nz any positive results should also be reported to the local health centre so that we can support follow up," she said.
Skinner is encouraging anyone on the island who isn't vaccinated or received their booster to do so.
"We encourage anyone who isn't vaccinated or hasn't had their booster to get vaccinated as soon as possible – the Chatham Islands Health Centre will be offering vaccinations tomorrow [Monday]."