Mr Hunt also said the rollout would begin with the vaccine developed by Pfizer and Germany's BioNTech, with priority being given to frontline workers in healthcare, hotel quarantine and border management.
Elderly people in aged care homes will also be amongst the first Australians to get the jab, pending its approval by Australia's Therapeutic Goods Administration.
In the interview published on Wednesday, Mr Hunt also said up to 80,000 doses a week will arrive in Australia from later this month.
The second major vaccine candidate - developed by AstraZeneca and Oxford University - is expected to be available for use in Australia by the end of March.
Both vaccines are already being distributed in the UK.
The UK has been inoculating people with the Pfizer vaccine for the past four weeks and on Monday became the first country in the world to start deploying the AstraZeneca vaccine.
The Pfizer vaccine is harder to manage than the AstraZeneca jab because it must be stored and transported at minus 70 degrees Celsius, while the latter can be kept in a refrigerator.
People in Australia must stay at least 1.5 metres away from others. Check your jurisdiction's restrictions on gathering limits.
If you are experiencing cold or flu symptoms, stay home and arrange a test by calling your doctor or contact the Coronavirus Health Information Hotline on 1800 020 080. News and information is available in 63 languages at sbs.com.au/coronavirus.
Please check the relevant guidelines for your state or territory: NSW, Victoria, Queensland, Western Australia, South Australia, Northern Territory, ACT, Tasmania.