NSW Health Minister Brad Hazzard said officials are now working to contact nearly 2,700 people who were also on that cruise and disembarked on Thursday, to ask them to self-isolate immediately.
"Our big concern, the very big concern, is that those people came off the cruise with no knowledge of COVID actually being on their ship," he said.
"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.
Mr Hazzard urged passengers to be aware of any symptoms, which may include fever or cough, and contact a GP or call the Coronavirus Health Information Line for advice.
Emails and SMS messages have been sent to passengers.
NSW chief health officer Dr Kerry Chant said the cruise ship company would take care of the 1100 crew members on the Ruby Princess.
The number of Australians among the crew remains unclear.
"They have doctors on board the ship, they have ICU facilities, they have care," Dr Chant told reporters.
"With all the passengers off the ship, they have the ability to reallocate all the crew to single rooms with bathrooms."
The three cases are among 75 new confirmed coronavirus diagnosis in NSW over the past 24 hours, bringing the state's total number of infections to 382.
SBS News has contacted Princess Cruises, which owns Ruby Princess, for comment.
Only people who have recently travelled from overseas or have been in contact with a confirmed COVID-19 case and experienced symptoms within 14 days are advised to be tested.
If you believe you may have contracted the virus, call your doctor, don’t visit, or contact the national Coronavirus Health Information Hotline on 1800 020 080.
If you are struggling to breathe or experiencing a medical emergency, call 000.