The Pacific Dawn has already been blamed for an increase in flu cases after authorities last week allowed all the passengers to leave the ship in Sydney despite a suspected outbreak on board.
At least 20 people were subsequently diagnosed with the virus and their presence in the community is believed to have contributed to the virus' spread, with the number of cases in Australia spiking in recent days to stand at 103.
"We are working very hard to contain this," Roxon told reporters in the capital Canberra after the confirmed number of cases jumped from 61 on Wednesday.
Health experts meanwhile have warned that Australia's rapidly rising number of flu cases could become an epidemic affecting up to 25 per cent of the population.
|There is growing alarm in Australia over the rapid rise of H1N1 flu cases [EPA]
In an effort to contain the outbreak the government has ordered 10 million doses of a H1N1 flu vaccine.
Roxon said the government would also buy a further 1.6 million courses of Relenza, an antiviral drug to bolster the national stockpile to 10.3 million courses.
Most cases of H1N1 flu were located in the country's most populous states of New South Wales and Victoria, which are heading into the winter season.
The supply would cover just less than half of Australia's 21 million people, but Roxon said medical authorities would prioritise which areas and people would most need the vaccine.
According to the World Health Organisation, the number of H1N1 cases has soared to nearly 13,400 case in 48 countries, with 100 deaths.