Tourism Bay of Plenty was trying to determine the movements of the passengers on the cruise.
The Ministry of Health said in a statement the passenger, an Auckland man in his 60s, was one of the confirmed cases announced on Friday.
He joined the cruise in Auckland on March 10 and departed it in Dunedin on March 15 before making his own way back to Auckland.
The ship visited Tauranga, Picton, Akaroa and Port Chalmers, and left Fiordland on March 16.
The ship arrived in Sydney this morning and every person on the Celebrity Solstice who is now in New Zealand will be regarded as close contacts, put in self-isolation and monitored daily.
They should also register online with Healthline.
If any passenger has symptoms they should call Healthline 0800 358 5453 for advice.
The Ministry of Health said public health staff would be working with their counterparts in Australia, giving details of the activities of the passenger while onboard the cruise.
This was to help Australian health services follow up contacts.
All cruise ships have been banned from coming to New Zealand until at least June 30.
Ships already in New Zealand waters are allowed to finish their itinerary.
• Covid19.govt.nz: The Government's official Covid-19 advisory website