As many as 30 people have been injured on board what passengers have described as "the cruise from hell".
The Carnival Legend cruise was forced to make an impromptu stop at Eden Port on the country's south coast so police officers could remove the violent men.
The brawl broke out in the early hours of Friday morning aboard the ship which was well into its 10-day cruise around the South Pacific.
Video of the scuffle, shared on social media, shows dozens of people fighting each other, security guards and other staff before the person filming the incident is confronted by staff.
Zac claimed the drama between his family and another party began when someone had stepped on a "thong" - the Aussie word for a flip-flop shoe.
They were then transported to Canberra Airport, where other travel arrangements were made, police say.
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Carnival has dispatched a "care team" to support the remaining passengers who are due to finish their cruise in Melbourne on Saturday.
Travelling with her partner and another couple, she said their group became targeted two days ago after one member accidentally brushed past a member of the "violent" family.
His 20-year-old son said "a lot of people are bleeding, a lot of people down".
"He said: 'Please, Dad, please Dad, call the federal police".
'I could hear a lot of screaming, crying in the background'.
David Barkho says his son phoned and begged him to call authorities after he suffered a head injury while on the ship. Police confirmed that security detained the men involved.
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She added there had been a number of fights on board, including in a nightclub and in an elevator the next day, "and a big fight on the lido deck, which went on for about 45 minutes".
Police said six men and three teenage boys were removed from the ship and that a further 14 passengers, including women and children, also left the ship.
One woman yelled that she had been mistreated as she was being removed after what fellow passengers complained had been days of mayhem and violence.
Jennifer Vandekreeke, Carnival Cruise Line vp and gm Australia, issued a statement saying that the safety and security of passengers and crew is the company's No. 1 priority.
"The ship's highly trained security staff have taken strong action in relation to a small group of disruptive guests who have been involved in altercations on board", the statement continued.
"We apply a zero-tolerance approach to excessive behaviour that affects other guests".
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