Louise Beamont, 31, who goes by the stage name Reay, has been accused by Thomas Reay of defamation and breach of privacy after her show last August.
Mr Reay is seeking £30,000 in damages plus legal costs and has instructed lawyers to pursue his claim.
He also wants an injunction to prevent her publishing statements about him, she said. The pair married in 2013 but broke up before she wrote Hard Mode – a show about freedom of speech which mentions her previous relationship.
But Ms Beamont, winner of the 2015 Alternative New Comedian of the Year, now fears being bankrupted should she loses the case.
She has launched a fundraising page to help pay for her defence.
On her Gofundme page, she wrote: “It was a 50-minute show about censorship and authoritarianism, asking the audience to imagine that the BBC had come into the control of the Chinese government.
“During that show, I referred to my husband a couple of times – perhaps two minutes’ worth of reference in a 50-minute show.
“The main gist of those references was to tell the audience how sad I was that my marriage had broken down recently.
“He is seeking £30,000 damages, his legal costs (which I can only assume will be massive) and an injunction stopping me from publishing statements about him.
“This is despite the fact that I gave him an undertaking (a sort of legal promise – without admitting liability of course) not to mention him in any further performances of the show, as soon as his lawyers complained.
“Indeed, all further performances of the show at the Edinburgh Fringe were without reference to him.”
For legal reasons, Ms Beamont, who lives in London, said she would not comment beyond her statement on the fundraising page. She added: “As stand-up comedians, I believe it’s the very definition of our job to talk about our lives and social issues.
“So this has become a free speech issue.”
But Mr Reay’s solicitors said they do not see this as a “free speech issue”.