About 2,700 passengers who disembarked a cruise ship in Sydney have been told to self-isolate after three people who were onboard tested positive for Covid-19.

Confirming the news on Friday, the NSW health minister, Brad Hazzard, said the doctor onboard had conducted 13 tests on the Ruby Princess, which had completed a relatively short cruise around the Pacific to New Zealand.

Two passengers who have tested positive are being treated in a Sydney hospital and another who may have contracted the virus made it to Tasmania and is in hospital there. A crew member who tested positive remains on the ship, which is anchored off the Australian east coast.

Guidelines introduced by the government this week mean people who had arrived from overseas were already required to self-isolate for 14 days. But Hazzard said authorities were now concerned that others may also have contracted the virus and that passengers were unaware there were confirmed cases onboard.

“The very big concern is that those people came off the cruise with no knowledge of Covid actually being on their ship,” he said. “If they think that it’s OK to be wandering around, the clear message from me as New South Wales health minister is ‘no it’s not’.

“Please put yourself into immediate quarantine for 14 days, self-isolate in your home or your normal place of residence, or whenever you may be, and start taking very serious note of your own health.”

The NSW chief health officer, Dr Kerry Chant, said the ship had been deemed “low-risk” because it was travelling from New Zealand to Australia. But she said that “for the abundance of caution” health authority ensured that all swabs taken on cruise ships were tested for Covid-19.

“SMS and emails have gone out to all of those passengers on that ship,” Chant said. “We will be contacting everyone by phone to confirm that they have understood the requirements around self-isolation, which they were instructed to do by the ship as well as Border Force officers when they disembarked from the ship.

The Ruby Princess is operated by the same company that runs the Diamond Princess, the major cruise ship that was badly hit by the coronavirus last month.

The government has banned cruise ships from docking in Australia but made special arrangements for the Ruby Princess and others to dock on Thursday.

A Princess Cruises statement reportedly said that those who tested positive were “among a group of guests and crew members who had reported flu-like symptoms during the cruise”.

“All, along with their cabin occupants, had been in isolation onboard the ship, which minimised any contact with other guests or crew.”

The cruise ship departed Sydney on 8 March for a 13-night cruise to New Zealand, but the journey was cut short when the government introduced new travel laws in response to the pandemic.