Lawyers for Iris de la Torre, a 30-year-old jewellery design student in London, accused the BBC of using racism to boost ratings and said the case could cost the corporation up to �1m in damages. They demanded an investigation by the BBC and suspension of the show.
The BBC has already received an official complaint from the Mexican ambassador, who demanded an apology for the broadcast's "xenophobic" and "offensive" content.
The remark was made by the presenter Richard Hammond, while his co-presenters, Jeremy Clarkson and James May, described Mexican food as "refried sick."
De la Torre's lawyers previously brought legal action against Channel 4 for remarks made about the Indian actor Shilpa Shetty in the reality show Celebrity Big Brother.
In a legal complaint seen by the Guardian and sent as a letter to the BBC, they claim that the remarks made on Top Gear are unlawful and a breach of the rules banning discrimination by public bodies.
"I was shocked at what the BBC allowed to be broadcast," De la Torre said. "I have never had a bad experience in the UK due to my nationality. I do not understand how such ignorant people hold such high-profile jobs."
The complaint could become the first case brought under the Equality Act, which came into force last September. Under the law, anyone providing a "service to the public" is prohibited from anything that constitutes discrimination.
Writing to the BBC is the first stage of bringing a case; the next would be making an application to a county court.
"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," said Lawrence Davies of De la Torre's solicitors, Equal Justice.
"However they are not permitted to use unlawful means to do so and broadcast their racist thoughts. A broadcast is a service and it is unlawful to produce racist services."
The BBC said it had not yet received the letter, but that it would be dealt with through the appropriate channels.
The controversy is the latest in a series of TV scandals involving offensive behaviour by presenters. Last month Sky Sports presenters Richard Keys and Andy Gray lost their jobs after sexist off-air remarks were leaked.
Top Gear presenter Clarkson, who has been repeatedly criticised for making offensive comments, had condemned Sky for the decision, describing it as "heresy by thought".
