However Hamas could have no role in its governance, Penny Wong said.
Both Australia's opposition and the Zionist Federation of Australia say such a move would be premature.
Canberra has long said that recognition of a Palestinian nation could only come as part of a two-state solution brokered with Israel.
But Ms Wong's comments echo a speech by UK Foreign Secretary David Cameron earlier this year, in which he hinted the UK too could recognise Palestinian statehood without the support of Israel.
The Australian government has in recent months increasingly voiced concerns about the war against Hamas in Gaza - including after an Australian aid worker was killed alongside six others in an Israeli air strike. The aid workers were travelling in a convoy after picking up supplies when the IDF says they were wrongly identified as Hamas operatives and targeted.
In a speech on Tuesday night, Ms Wong said a two-state solution - where Israelis and Palestinians lived side by side in separate countries - was "the only hope to break the endless cycle of violence".
"The failures of this approach by all parties over decades - as well as the Netanyahu government's refusal to even engage on the question of a Palestinian state - have caused widespread frustration," she said.
"So the international community is now considering the question of Palestinian statehood as a way of building momentum towards a two-state solution."
The opposition's foreign affairs spokesman, Simon Birmingham, said it did not support such a move and that Prime Minister Anthony Albanese's government was threatening to "break decades of bipartisan Australian foreign policy".
"The Albanese government's argument to pre-emptively recognise a Palestinian state puts statehood before security, and will be seen as a win by the terrorists who initiated the current horrific conflict," he said in a statement.
Zionist Federation of Australia president Jeremy Leibler said any talk of recognition of Palestinian statehood was "entirely premature".
"Before any talk of statehood is credible, Hamas must be removed and a new generation of Palestinian leadership must emerge, which isn't corrupt, don't condone violence and recognises Israel's right to exist as a Jewish state," he said.
However Ms Wong said claims that recognition of a Palestinian state would be "rewarding the enemy" were "wrong". Israel's security depends on a two-state solution, she said, and recognition of statehood would help undermine and marginalise Hamas.
About 140 countries recognise Palestinian statehood, but many including the US, the UK, Germany and Australia do not.
The United Nations is this week set to consider granting Palestine - which is currently an "observer state" - full membership of the international body.
The war in Gaza, Israel's response to a Hamas-led attack on 7 October that killed about 1,200 people and saw more than 250 taken hostage, has killed more than 33,000 Palestinians, according to the Hamas-run health ministry. Large parts of the territory are destroyed and many other Palestinians have been left on the brink of famine.
Weeks of talks have failed to produce an agreement but international pressure is growing.
By Tiffanie Turnbull