The one-hour stand-up show was being recorded as part of a Netflix special titled 'His Dark Materials', to which Carr issued a trigger warning to the audience.
Carr is reported to have addressed the audience, stating: "We are going to talk about cancel culture, the whole thing. We are going to talk about f***ing everything, people. Relax."
The 'joke' referred to the deaths of thousands of gypsies who were murdered during the holocaust.
Since airing, Carr has been subject to thousands of negative comments on social media - with many calling for him to be taken off the air.
The Traveller Movement – a charity supporting the traveller community in the UK – said: "This is truly disturbing and goes way beyond humour. We need all your support in calling this out."
Comedian David Baddiel spoke out on the material, suggesting the joke was "indefensible".
One viewer wrote: "It's estimated that around 75 per cent of Europe's gypsy and Roma population were murdered in the Holocaust. Take Jimmy Carr off the air and cancel all his projects immediately."
The Auschwitz Memorial called for Carr to "learn about the fate of some 23,000 Roma and Sinti deported to Auschwitz" in a tweet to their 1.2 million followers.
And Olivia Marks-Woldman OBE – the Holocaust Memorial Day Trust CEO – has also hit out at members of the audience.
"We are absolutely appalled at Jimmy Carr's comment about persecution … and horrified that gales of laughter followed his remarks," she said.