The Australian Muslim Advocacy Network has lodged the complaint against Twitter's global and Australian companies at the Queensland Human Rights Commission under Section 124(A) of the state's discrimination act.
"The action alleges that Twitter is liable as a publisher for vilifying third-party content," the network said on Monday.
It referred to similar actions in Australian courts involving Meta and Google.
Earlier this month, tech giant Google was ordered to pay former NSW deputy premier John Barilaro more than $700,000 over a series of racist and abusive videos published on a YouTube channel.
The advocacy network's complaint includes nearly 420 examples of "hate artifacts", including 29 tweets it says incite hatred and 390 comments and quote tweets.
These include recent tweets that openly disparaged newly elected Senator Fatima Payman in Western Australia.
Senator Payman is the first hijab-wearing elected representative in the federal parliament.
The network also alleges discrimination through bigoted misinformation.
"Disinformation portraying groups as subhuman or inhuman based on their religion or race has the effect of inciting hatred and therefore violates Australian standards," the network said.
Last year, the network was successful in forcing former Queensland senator Fraser Anning to remove 141 pieces of online content after a Queensland tribunal found he breached anti-discrimination laws by vilifying Muslims.
The advocacy group is calling on the federal government to penalise social media platforms that don't meet Australian vilification laws.
AAP has contacted Twitter for a comment.
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