The government's controversial ban, which made it an offence for people to try and re-enter Australia after being in India within the prior 14 days, began on Monday and was due to finish on 15 May.
Morrison said the National Security Committee met yesterday and agreed it saw "no need to extend it beyond that date".
"The original decision to put in place that biosecurity order until the 15th of May has proved very effective and it will run its full course until that time without any change," he said.
"What we will be doing is receiving our first repatriation flight into the Northern Territory as part of the charter arrangements we have … to bring back those first people from India at that time."
There are currently 9000 Australians in India who want to come home, with around 900 of them considered vulnerable.
Earlier, ABC political reporter Jane Norman reported the first repatriation flight would have the capacity to bring home around 200 passengers.
All Australians returning from India will quarantine outside Darwin at the Howard Springs facility, which was expected to be nearly empty by next Saturday, Norman reported.
Around 900 Australians who have been listed as "vulnerable" by the Department of Foreign Affairs will be given priority, the ABC said. But they will need to return two negative Covid-19 tests before they are allowed to fly.
Before the government imposed the travel ban, it had been chartering two flights to India each week to bring Australians home. The ABC has been told there would be a maximum of one repatriation flight per week once travel resumes.
It is unclear whether commercial flights will also be able to restart, with one government source saying it would be a slow and steady process.
On Thursday, Immigration Minister Alex Hawke warned the repatriation process was "very complex" and would "take some time".
"This second wave is very bad, the logistics in India are very difficult, people are living in remote towns and villages and to get them safely to an airport is a very difficult undertaking," he said.
"These are the real, practical consequences. There are thousands of people, many dying on the streets in India. So it's going to be very complex."