told all the MPs running to lead the party.
Director general Carolyn Fairbairn told BBC Radio 4's Today programme that a no-deal Brexit should be an option "that is not even considered".
She was speaking after the CBI sent an open letter to candidates.
In its letter the CBI says: "Firms large and small are clear that leaving the EU with a deal is the best way forward."
"Short-term disruption and long-term damage to British competitiveness will be severe if we leave without one. The vast majority of firms can never be prepared for no-deal, particularly our [small and medium-sized] members who cannot afford complex and costly contingency plans."
She told Today that businesses were not ready for a no-deal scenario and said "this idea that we are ready is just not true".
"How can you be prepared for £20bn of increased customs costs? How can be you prepared for tariffs rising overnight? 150,000 businesses with no systems in place to do deal with this.
"This is not a responsible strategy for a government to have."
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The UK had been due to leave the EU on 29 March, but Theresa May asked for an extension and the date was pushed back to 31 October.
The official race to succeed her gets under way after she stands down in early June, but jostling between Tory candidates has already begun.
Esther McVey, the first of the 12 confirmed contenders to stand in the Tory leadership race, said earlier this week in a column for the Daily Telegraph the UK needs to "actively embrace leaving the EU without a deal".
Former Foreign Secretary Boris Johnson and ex-Brexit Secretary Dominic Raab have said they would like to renegotiate the terms of Mrs May's withdrawal agreement with Brussels, but would enforce the current October deadline.
Gerard Lyons, co-founder of Economists for Brexit, told Today: "I don't think any of the leadership candidates are advocating no deal as their plan A.
"One has to have a plan B. No deal, whether we like it or not, has to be plan B.
"The CBI, remember, was amongst Project Fear three years ago and since the referendum we've seen one million jobs added the economy," he said.
Mr Lyons, a former advisor to Mr Johnson, told the BBC a no-deal Brexit would just be a "stepping stone" to a free trade agreement.
He said the challenges facing the UK would be "better addressed outside" the EU and that a focus needed to place on issues such as investment in infrastructure and investment to address "imbalances" in the economy.
British business has issued a challenge to the next prime minister to prove that the Conservatives are the party of business. That can only be achieved, says the CBI, if the next leader commits to leaving the EU with a deal.
The lobbying group insists that firms large and small are clear that leaving the EU with a deal is essential to protect the economy, jobs and living standards.
However, of the 12 candidates (so far), at least half say they are prepared (in fact some of them are determined) to leave the world's largest trading bloc as scheduled at the end of October - with or without a deal in place.
That includes the current favourite, Boris Johnson who, when foreign secretary, had a message for business leaders during the Brexit negotiations that ended in "ck" but wasn't "back".
That expletive - directed to a community that had traditionally seen the Conservative Party as its natural partner - shocked some in the business world and for others merely highlighted the dwindling influence of business in the politics of Brexit.
That gulf still seems very wide with business saying it can't work with anyone who contemplates no deal - and a party which may find it hard to contemplate a leader who won't.
Business has traditionally been important to the Conservative Party as one of its main sources of financial support.
However, overall donations to the party collapsed in the first quarter of the year, according to figures published by the Electoral Commission. The party received £3.7m in donations and public funds in the three months to March. For the fourth quarter of 2018, it was £7.5m.
Tory leadership candidate Jeremy Hunt has warned his party that pushing through a no-deal Brexit would be "political suicide" because it would result in a general election in which Labour could take power.
Fellow leadership contender Kit Malthouse, a housing minister, has said: "Those people who say no-deal would be a catastrophe and those people who say it would be a walk in the park are both wrong - it is somewhere in the middle."
Meanwhile, the EU's chief Brexit negotiator Michel Barnier has said the deal reached between the UK and the EU was "the only option" if the UK wanted to leave "in an orderly manner".
Who will replace Theresa May?
The winner of the contest to lead the Conservative Party will become the next prime minister.