Former NRL player Joe Williams shared the old clip over the weekend, arguing Noah's comments were "unacceptable". Williams – who is Wiradjuri – has been vocal about Indigenous rights in the past as well as issues such as mental health.
"You are perpetrating and encouraging racial abuse," he said.
Noah's comments about Aboriginal women received widespread backlash, with calls to boycott his forthcoming shows.
The comedian eventually responded to the criticism, telling Indigenous writer Dr Anita Heiss he should have known better.
"After visiting Australia's Bunjilaka museum and learning about Aboriginal history firsthand, I vowed to never make a joke like that again," he wrote on Twitter. "And I haven't. I'll make sure the clip from 2013 is not promoted in any way."
The controversial clip has been since been deleted from YouTube.
Noah recently made headlines after joking it was Africa that won the World Cup, not France. The jibe drew the attention of France's ambassador to the United States, Gerard Araud, who sent the comedian a strongly-worded letter.
Noah was born in South Africa to a white father and a black mother, and rose to international prominence as a correspondent for Comedy Central's The Daily Show.
In 2015, he took over hosting duties after Jon Stewart retired. The comedian's contract has him hosting the show until at least 2022.
The Daily Show host will be touring Australia next month. He will perform stand-up at Melbourne's Hisense Arena on Thursday, August 23 followed by shows in Perth, Brisbane and Sydney's International Convention Centre.
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