As of midnight last Saturday, all cruise ships were banned from coming to New Zealand until at least June 30.
Ships already in New Zealand waters were permitted to conclude their itinerary.
The Ministry of Health said public health staff will be working with their counterparts in Australia, giving details of the activities of the passenger while onboard the cruise.
This was to assist the Australian health services in the follow up of contacts.
The ship arrived in Sydney this morning and any New Zealanders on board returning to New Zealand will be regarded as close contacts, put in self-isolation and monitored daily.
The ministry has said every person who was on the Celebrity Solstice who is now in New Zealand needs to self-isolate now and register online with Healthline.
They will be followed up as a close contact.
If any passenger has symptoms they should call Healthline 0800 358 5453 for advice.
56 New Zealanders on board cruise ship with four confirmed cases
The Ministry of Health says 56 New Zealanders were on board an Australian cruise ship where four people tested positive for Covid-19.
The Ruby Princess left New Zealand five days ago and docked in Sydney on Wednesday.
Three Australian passengers and one crew member were confirmed to have the potentially deadly virus.
The Ministry of Health say they are in the process of contacting all New Zealanders who were on board the ship. The advice will be to be vigilant and contact their GP or Healthline if they display any COVID-19 symptoms.
The cruise ship departed Sydney on March 8. Any passengers on the cruise, who had since returned to New Zealand would be covered by the requirement since March 15 for all travellers returning to New Zealand to go into self-isolation for 14 days.