India has seen soaring infection rates, a rapidly rising death toll and the discovery of a new virus variant.
Mr Hunt made the unprecedented determination under the Biosecurity Act after receiving advice from Chief Medical Officer Paul Kelly.
"The Government does not make these decisions lightly", Mr Hunt said.
Any change to allow travellers to start coming back will be based on the epidemiology in India, public health risk in Australia and quarantine capacity, Mr Hunt said.
The government will reconsider the restrictions on May 15. India's new coronavirus cases stayed above 300,000 for a sixth consecutive day on Tuesday.More news: Ontario government wants hotel quarantine for land border crossings too
Returning residents and citizens have to undergo a mandatory two-week hotel quarantine at their own expense, a system that has largely helped Australia to keep its COVID-19 numbers relatively low, with just under 29,700 cases and 910 deaths.
The ministry statement said it is important that the integrity of the Australian public health and quarantine system are protected and the number of COVID-19 cases in isolation facilities is reduced to a manageable level.
Australia will also provide to India emergency medical supplies, including over 1,000 non-invasive ventilators.
A wreath lies on the coffin of a Covid-19 victim prior to cremation in Jammu, northern India.
More than 9000 Australians in India are registered as wanting to return, including 650 people registered as vulnerable.
Some cricketers - who went over last month for the Indian Premier League - are among those stranded.More news: Which six states gained Congressional seats; which seven lost seats?
India recorded 360,960 new infections in the last 24 hours, the largest in a single day taking the country's tally of infections to almost 18 million.
Neela Janakiramanan, an Australian surgeon with family in India said the decision to "criminalise" Australians returning from India was disproportionate and overly punitive.
He said National Cabinet wanted flights from India restarted "as soon as possible" after the May 15 reassessment date. "Tragically, many are contracting COVID-19 and many, sadly, are dying every day".
"National cabinet expressed solidarity with the Indian community both within Australia and overseas", Australian Prime Minister Scott Morrison said in a statement yesterday, not fronting the media after the meeting.
Another 386,452 infections and 3,498 deaths were officially recorded on Friday - but medics have warned the true figures could be ten times greater, putting daily infections at three million.
Several countries from around the world are sending much-needed supplies to India.More news: India virus patients suffocate amid oxygen shortage in surge