There have been at least 600 COVID-19 cases, including passengers and staff, associated with the vessel, and 11 have died.
As a popular Pacific port destination, Australia is among numerous countries around the world negotiating arrangements with cruise ships unable to find somewhere to dock.
NSW Police said in a statement on Monday that the vessel may remain in place for up to 10 days, but the crew will not disembark unless approved by state authorities.
Sick crew members were being treated onboard or transferred to hospital, police said, and the vessel will be refuelled in preparation for departure.
An investigation into Ruby Princess protocols will focus on communications and actions that led to the docking and disembarking of the ship’s 2,700 passengers on March 19 at Sydney Harbour to see whether biosecurity laws or state laws were broken, authorities said.
State health authorities had classed the ship as low risk, and the Australian Border Force issued a notice allowing the passengers to travel home freely. They were required to self-isolate for 14 days.
A Carnival Australia spokesman said on Monday the company would cooperate with the probe.
The ship has remained in Australian waters and on Monday docked at Port Kembla, with the remaining crew from 50 different countries on board to stay in isolation.
The government banned cruise ships from docking except for emergencies as of mid-March and has sent off most of the cruise ships that remained in Australian waters over the past week.