The decision comes after federal Tourism Minister Simon Birmingham said Australia's border for overseas travel would likely reopen next year.
Qantas signalled flights could resume if travel between Australia and other countries opened up.
"With Australia's borders set to remain closed for some time, we have cancelled most international flights until late October," a Qantas spokesperson said in a statement to AAP early on Thursday.
"We still have some flights scheduled across the Tasman in the coming months, with the expected travel bubble between Australia and New Zealand.
"Should travel between Australia and other countries open up and demand returns, we can add more flights back into our schedule."
On Wednesday Mr Birmingham encouraged Australians to holiday domestically, with international travel forbidden for the foreseeable future due to the coronavirus threat.
He said the government might eventually look at short-term overseas travel to countries other than New Zealand that have similar success in suppressing coronavirus.
"I do, sadly, think that in terms of open tourist-related travel in or out of Australia, that remains quite some distance off, just because of the practicalities of the volumes that are involved and the need for us to first and foremost keep putting health first," he told the National Press Club.
Asked whether that was more likely to resume next year, he said " I think that is more likely the case".
