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 in August last year.
Mr Reay is seeking £30,000 in damages plus legal costs and has formally instructed his 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 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.
And she has now launched a fundraising page to help fund her defence.
On her Gofundme page, the comedian 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 stays in London, said she did not comment beyond her statement on the fundraising page.
She added: “As standup 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 do not see this as a “free speech issue”.
Writing on behalf of her estranged husband, Taylor Hampton Solicitors Limited wrote in a statement: “This is not a “free speech issue”, and contrary to how Ms Beamont (also known by her stage name Louise Reay) presents our client’s legal complaint on her fundraising page, there is no question of any censorship taking place.
“We have from the outset made clear to Ms Beamont that our client is not in any way seeking to restrict or “silence” her comedy or its content, except to the very limited extent that it involves the publication of unjustified false allegations and private information relating to him.
“For an extended period last summer, following their separation, Ms Beamont repeatedly performed a comedy show which identified our client verbally and in still and moving images, contained private information about him and his relationship with Ms Beamont, and made very serious and inflammatory allegations of wrongdoing against him.
“These allegations included the entirely false suggestion that our client’s relationship with Ms Beamont was an abusive one.
“At no stage was our client asked for his consent or given any chance to put his side of the story.
“This was a highly personal attack on our client with no justification whatsoever.
“He was harassed by the performances, and their content and its repeated publication from the very public platform of Ms Beamont’s live performances caused him enormous distress.
“No right to freedom of expression or artistic licence can extend to the publication of such seriously defamatory and false allegations, or the unjustified misuse of our client’s private information, and, six months later, Ms Beamont has yet to make any coherent defence of what she published about him.
“Our client has made every effort to resolve this dispute amicably.
“However, Ms Beamont appears determined to continue making the same allegations about him.
“He deeply regrets that it has been necessary for him to bring these proceedings, but he has been left with little choice but to attempt to protect himself.”