Carolyn Fairbairn said the lack of a clear Brexit plan meant firms were having to prepare for a no-deal outcome but tens of thousands of companies had "no systems in place" to cope with a World Trade Organisation approach.
Government minister Edward Argar insisted a no-deal scenario would not be a "catastrophe" although he acknowledged it would not be perfect either.
Ms Fairbairn said the view of CBI members was "frustration bordering on despair" at the "soap opera" in Westminster.
"I think there are now six different ideas for a future Brexit direction which means that if you're running a business at the moment you can only plan for one outcome and that is a no-deal scenario and that is what we're seeing," the CBI director-general told BBC Radio 5 Live's Pienaar's Politics.
There was an "alarming" question about the "future attractiveness of the UK because we are looking so unpredictable at the moment".
She said the UK had to get behind a plan "and the Government's white paper had a lot of what business needed in it".
Ms Fairbairn said the Chequers plan "is not perfect" but "it is a good framework", although services firms would like a closer relationship with the EU than set out in the proposals.
Setting out the risks of a no-deal Brexit she said: "There are 150,000 businesses out there that have only ever traded with the European Union, they have no systems in place, they have no ability to be able to deal with WTO rules, they have no ability to be able to get their stuff across borders.
"There are many businesses who don't know if their goods would be legally tradable in a no-deal world.
"This is an incredibly serious thing to be considering as a possibility, I think because we are so close to it now, it would be a catastrophe and it really should be taken off the table by both sides."
Mr Argar said the Government was "working very hard to get a deal" but repeated Theresa May's mantra that "a no-deal scenario is better than a bad deal".
He told the programme: "Leaving with no deal would not be broad, sunlit uplands and everything perfect but equally I don't think it would be a catastrophe."