She says she will take "whatever legal action is necessary" unless The Stand admits that it acted unlawfully, issues an apology and reinstates the event.
The venue had cancelled the show after staff said they were not comfortable with her views on transgender issues.
The Stand has not yet responded to Ms Cherry's comments.
The Edinburgh South MP had been due to take part in a series of In Conversation With... events in August.
Ms Cherry is a critic of Scotland's gender recognition reform plans, which make it easier for people to change their legally-recognised sex.
Last week she told BBC Scotland she felt she had been "cancelled and no-platformed" because she was a lesbian who holds gender-critical views.
She said she had been "greatly heartened" by the support she had received since the story became public, and had decided to seek legal advice.
"I am prepared to take whatever legal action is necessary to vindicate my right not to be misrepresented and not to be discriminated against," she said.
"This is not about money. My primary goal is to have the actions of The Stand acknowledged as unlawful and to ensure the event proceeds.
"I have asked The Stand to apologise to me too. If they don't agree with my reasonable requests, I intend to ask the court to decide on the issue."
Ms Cherry said the decision to cancel her show was symptomatic of a wider problem in society.
"I am very concerned that those who hold perfectly legitimate views on a variety of issues, including women like me, are regularly being misrepresented, de-platformed and, in some cases, facing damage to or the loss of our livelihoods," she added.
"This is often accompanied by online abuse and threats.
"The debate on gender self-identification is a very important one which must be allowed to take place, but I am a woman of many parts who was engaged to talk about my political life in general and I see the cancelling of my one-hour event as the thin end of the wedge."
Last week The Stand said that a number of its key operational staff, including venue management and box office personnel, were unwilling to work on the event.
"We will ensure that their views are respected," it said in a statement.
"We will not compel our staff to work on this event and so have concluded that the event is unable to proceed on a properly staffed, safe and legally-compliant basis.
"We advised the show producers, Fair Pley Productions, of this operational issue and they advised Joanna Cherry that it is no longer possible to host the event in our venue."
The Stand - which was co-founded by SNP MP Tommy Sheppard - said it did not endorse the views of any participant in the In Conversation With... series, which is organised by independent producer Fair Pley.