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The case was revealed by the ministry yesterday and whether it was a historical case or a false positive test result is being investigated.
As a precaution, the Rakiura Rugrats early childhood centre has been closed for the rest of the week.
Director-general of health Dr Ashley Bloomfield said yesterday the case was a child and it was likely the result was a false positive
"Serology testing of the adult household contacts of the person on Stewart Island/Rakiura has been completed and the results have come back negative," the ministry said today.
A further Stewart Island update will be included in the ministry's 1pm statement today.