A group of five Australian lawyers have filed a private application in the Melbourne Magistrates Court seeking to prosecute her over the treatment of the Muslim-minority Rohingya.
It coincides with the Nobel laureate attending a special summit of Southeast Asian leaders in Sydney.
Myanmar's Suu Kyi makes first visit to crisis-hit northern Rakhine
Nearly 700,000 Rohingya have fled Myanmar's troubled Rakhine state for Bangladesh since authorities launched a brutal crackdown six months ago that the UN has called "ethnic cleansing".
Myanmar has vehemently denied the allegations, insisting it was responding to attacks by Rohingya militants in late August.
Attorney General Christian Porter said Suu Kyi cannot be prosecuted in Australia, nor arrested or detained.
"Aung San Suu Kyi has complete immunity," he said in a statement.
"This includes from being served with court documents because under customary international law, heads of state, heads of government and ministers of foreign affairs are immune from foreign criminal proceedings and are inviolable."
Suu Kyi has come under intense global criticism for her public silence on the atrocities in Myanmar, which include claims of rape, murder and arson.
The private prosecution alleges she committed crimes against humanity by the deportation and forcible transfer of the Rohingya people.
Aung San Suu Kyi should quit over deadly campaign against Rohingya Muslims, says U2 frontman
One of the lawyers involved, Alison Battison, told the Sydney Morning Herald that Porter's decision was appealable.
"The Attorney General is yet to respond to us, but when he does, we'll address that then," she said.
"We wouldn't have done it if we didn't think we had a chance ... it's a textbook example of crimes against humanity."
Suu Kyi has not commented publicly since arriving in Australia on Saturday for the regional summit, but is scheduled to take questions at a media event on Tuesday.
Malaysian Prime Minister Najib Razak ramped up pressure on her Saturday when he said the Rohingya issue could threaten regional security.
China to host Myanmar's Suu Kyi in Beijing amid global outcry over Rohingya exodus
Speaking in Sydney with Suu Kyi sitting just metres away, he warned that many desperate people could fall prey to extremist groups like Islamic State.
"Because of the suffering of Rohingya people and that of displacement around the region, the situation in Rakhine state and Myanmar can no longer be considered to be a purely domestic matter," he said.
"In addition, the problem should not be looked at through the humanitarian prism only because it has the potential of developing into a serious security threat to the region."
He added that Malaysia was ready to assist in finding "a just and durable solution", but did not spell out what that might involve.
Suu Kyi is due in Canberra on Monday for bilateral talks with Australian Prime Minister Malcolm Turnbull before an address to Sydney's Lowy Institute on Tuesday.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ