The temporary emergency determination, issued late on Friday, is the first time Australia has made it a criminal offence for its citizens to return home.
The move was prompted after two people circumvented travel bans from India, returning to Australia via Doha in a loophole that has since been closed.
It is also the first time in history the Australian Government has used any kind of emergency powers for that objective.
"The risk assessment that informed the decision was based on the proportion of overseas travellers in quarantine in Australia who have acquired a COVID-19 infection in India", Mr Hunt said in a statement.
"The Government does not make these decisions lightly", Mr Hunt said. "Tragically, many are contracting COVID-19 and many, sadly, are dying every day", Hunt said.
The government will reconsider the restrictions on May 15.
Australians defying the travel ban and flying both directly and indirectly from India could be fined or imprisoned.
Morrison said the suspension would provide a "breather" to quarantine facilities in New South Wales state and the Northern Territory, given the majority of positive cases there came from India.
More than 9000 Australians in India are registered as wanting to return, including 650 people registered as vulnerable.
For over a week, India has reported more than 300,000 new Covid-19 cases a day, with the total infections since the start of the pandemic nearing 19 million.
India's spiralling coronavirus crisis was today laid bare as images circulated on social media of the bodies of 22 coronavirus victims stuffed into an overloaded ambulance to be taken to the crematorium. Almost 9,000 Australians are now stranded in India, according to ABC News.
Kenya is still experiencing a third wave of coronavirus infections, though cases and infection rates have tapered off in recent weeks.
Australian cricketers Adam Zampa and Kane Richardson were among those who dodged the restriction after leaving the Indian Premier League.
But the relieved pair managed to get tickets to Doha on Wednesday before securing seats on a chartered flight back to Australia.
The Kenya Medical Practitioners and Dentists Council on Wednesday released a list of 10 isolation facilities for passengers who will be arriving in the country from India.
About 36,000 Australian citizens overseas are registered with the government to receive assistance returning home.
Failing to comply with the temporary pause may result in a fine of $66,600 or five years' imprisonment, or both, Mr Hunt said.
Health Minister Mutahi Kagwe said Kenya had "observed the dire events in India. and resolved to suspend all passenger flights in and out of the country for a period of 14 days".