Lawyers for Iris de la Torre, a 30 year-old jewellery design student, said the BBC had used racism to boost ratings and could cost the Corporation up to £1million in damages.
In the episode, which was viewed by more than 6 million people, Richard Hammond claimed that cars imitate national characteristics.
"Mexican cars are just going to be a lazy, feckless, flatulent, oaf with a moustache leaning against a fence asleep looking at a cactus with a blanket with a hole in the middle on as a coat," he said.
Jeremy Clarkson went on to joke that being Mexican would be "brilliant" because then he could sleep all day.
The Mexican ambassador to Britain has already made an official complaint to the BBC for the programme's "xenophobic" and "offensive" content and demanded an apology.
De la Torres' lawyers, from the firm Equal Justice, also brought legal action against Channel 4 following remarks made about Shilpa Shetty during Celebrity Big Brother.
In a legal complaint to the BBC they claim that the remarks are unlawful and a breach of rules banning discrimination by public bodies, according to a report by The Guardian.
De la Torre said: "I was shocked at what the BBC allowed to be broadcast...I do not understand how such ignorant people hold such high-profile jobs."
If taken to court it could become the first case to be brought under the Equality Act which came into effect in September last year.
Lawrence Davies, from Equal Justice, said: "These remarks were probably calculated and deliberate to fuel anger and hence boost ratings - the presenters apparently feel that they are fighting a battle against political correctness."
The BBC said it had not yet received the legal letter but said that it would be dealt with through appropriate channels.
The Telegraph
