Writing in The Telegraph, the former Ukip leader, now affiliated with the new Brexit Party, said an extension of Article 50 would be seen as a betrayal by millions of voters.
“Any extension of Article 50 will be seen as a betrayal of our nation by millions of angry Conservative voters,” he said.
“The choice facing Theresa May is simple. If she holds firm and abides by the law of the land, Britain will leave the European Union at 11pm on 29 March.
“If she buckles, and a long extension ensues, I promise I will do my best to tear her party limb from limb. It deserves no better.
“It is time we left the European Union and got on with the rest of our lives.”
Mrs May today asked the EU to allow the UK's withdrawal date to be delayed to June 30 and threatened to resign as Prime Minister if MPs demand a longer postponement.
European Council President Donald Tusk then said the EU would grant a "short extension" but only if MPs back the Prime Minister's deal in the Commons during a third meaningful vote next week.
In the Commons on Wednesday, Mrs May set out plans to prevent Speaker John Bercow blocking a third vote on her deal, which was rejected by MPs by 230 votes in January and 149 votes earlier this month.
Mr Farage wrote on Wednesday: “As the Prime Minister heads to tomorrow’s EU summit in Brussels with little prospect of achieving her desperate attempt to engineer a short-term Article 50 extension, I want to give her something else to think about: the survival of the Conservative Party.”
Mr Farage added: “I do wonder how Number 10 has got things so wrong. "
Mr Farage said that by applying for an extension to Article 50, Mrs May was doing damage to Britain's global standing as a democratic nation."
“For we are diminished, shredded, and now look something like a banana republic," he said.