They are looking into whether biosecurity laws have been broken when Ruby Princess guests were allowed to get off the vessel in Sydney with flu-like symptoms.
Since then, more than 600 people have tested positive for Covid-19 and 10 people have died, the BBC said.
Ruby Princess remains docked off the coast with nearly 200 unwell crew members onboard.
At a press conference, New South Wales police commissioner Mick Fuller revealed a criminal investigation has been launched.
“The only way I can get to the bottom of whether our national biosecurity laws and our state laws were broken is through a criminal investigation,” he said.