Hundreds of public figures with Jewish heritage who were members of a private WhatsApp group had their names, photos and social media accounts published online by pro-Palestinian activists.
In response, Attorney-General Mark Dreyfus is exploring laws that would address doxing and strengthen hate speech protections.
The government's online safety watchdog defines doxing broadly as "the intentional online exposure of an individual's identity, private information or personal details without their consent".
Asked for his definition, Mr Dreyfus said it was "the malicious release, publicly, of personal information of people without their consent".
"The recent targeting of members of the Australian Jewish community through those practices like doxing was shocking but sadly, this is far from being an isolated incident," he told reporters in Canberra on Tuesday.
"We live in a vibrant, multicultural community which we should strive to protect.
"No Australians should be targeted because of their race or because of their religion."
The possible changes would use the eSafety Commissioner's provisions to send takedown notices to social media sites and impose penalties, alongside other measures.
While opposition cyber security spokesman James Paterson supported the proposed laws, he said press freedoms must be taken into consideration.
"I'm sure it can be drafted in a way that both protects the community from this insidious and dangerous practice and preserves press freedom," he told reporters.
The Executive Council of Australian Jewry welcomed the government's plan to make doxing a crime.
"We look forward to working with the government to ensure the full extent of the harm caused is understood and that the new laws effectively protect Australians from this shameful and dangerous practice," council president Daniel Aghion said.
Prime Minister Anthony Albanese on Monday said the doxxing that took place was completely unacceptable.
"This is not the Australia that we want to see," he said.
"These are 600 people in the creative industries, people like Deborah Conway the singer, people who are in the arts and creative sector, who had a WhatsApp group.
"Not a WhatsApp group that was heavily political, a WhatsApp group to provide support for each other because of the rise in anti-Semitism that we've seen.
"And what we've seen is them being targeted."
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