0401 GMT June 21, 2018
Paul Dreschler also said there was ‘zero evidence’ that trade deals outside the EU will provide any economic benefit to Britain, according to BBC.
But the government said it was "focused on delivering a Brexit that works for the whole of the UK".
Brexit campaigners said the CBI was "the voice of vested interests".
"If we do not have a customs union, there are sectors of manufacturing society in the UK which risk becoming extinct," Dreschler said.
"Be in no doubt, that is the reality."
He told BBC Radio 4's Today program the automotive industry in particular would suffer unless we get ‘real frictionless trade’.
Dreschler, who is due to step down from his role next week, said greater costs caused by the imposition of trade tariffs and delays at the border will not only affect individual companies, but the entire supply chain.
He added that the UK would be much better using the scale of the EU to negotiate trade agreements than going it alone.
"There's zero evidence that independent trade deals will provide any economic benefit to the UK that's material. It's a myth," he said.
'Lack of clarity'
Delays to business investment were also affecting the UK economy, he said.
"We already know tens of millions, in fact hundreds of millions have been invested by UK pharmaceutical and finance companies to create continuity post a worse-case Brexit scenario. Tens of millions. What could we have done with that money?" Dreschler said.
The government has not given business the necessary clarity to make investment decisions, he said.
"We have a negotiation within the UK government that's gone on for nearly three years.
"We still haven't got clarity about the future direction, about where we're heading, what will be the future relationship with Europe, at a level of detail that matters for investment."
However, a spokesperson for the Department for Exiting the EU (Dexeu) said the government was "focused on delivering a Brexit that works for the whole of the UK — including businesses across the economy."
"We have laid out our approach to our withdrawal and future relationship with the EU in 14 detailed papers we published last summer, numerous speeches given by the prime minister and cabinet ministers, and the technical notes and slides we published in recent weeks.
"We'll soon publish a White Paper with detailed explanations of our ambition for a future relationship with the EU — building on the positions set out by the prime minister," the spokesperson added.