The UK "would regret it forever" if it lost its status as a world leader in car manufacturing after Brexit, Business Secretary Greg Clark has said.
He added it was "concerning" that Toyota UK had told the BBC that if Britain left the EU without a deal it would temporarily halt production at its factory in Burnaston, near Derby.
"We need a deal," Mr Clark said.
The Japanese carmaker said the impact of border delays in the event of a no-deal Brexit could cost jobs.
The Burnaston plant - which makes Toyota's Auris and Avensis - produced nearly 150,000 cars last year of which 90% were exported to the rest of the European Union.
"My view is that if Britain crashes out of the EU at the end of March we will see production stops in our factory," said Marvin Cooke, Toyota's managing director at Burnaston.
BMW, for example, says it will close its Mini plant in Oxford for a month following Brexit.
The main concerns relate to what carmakers say are supply chain risks in the event of a no-deal Brexit.
Toyota's production line is run on a "just-in-time" basis, with parts arriving every 37 minutes from suppliers in both the UK and the EU for cars made to order.
If the UK leaves the EU without a deal on 29 March, there could be disruption at the border which the industry says could lead to delays and shortages of parts.
It would be impossible for Toyota to hold more than a day's worth of inventory at its Derbyshire plant, the company said, and so production would be stopped.
'Keep jobs in the area'
Mr Clark said Theresa May's Chequers plan for future relations with the EU is "precisely calibrated to avoid those checks at the border".
"We need to have a deal... we want to have the best deal that will allow as I say not just the success at present to be enjoyed but for us to grasp this opportunity," he told BBC Radio 4's Today programme.
"The evidence from not just Toyota but other manufacturers is that we need to absolutely be able to continue what has been a highly successful set of supply chains."
Toyota was unable to say how long production would be stopped, but in the longer term, warned that added costs would reduce the plant's competitiveness and eventually cost jobs.
Peter Tsouvallaris, who has worked at Burnaston for 24 years and is the Unite union convenor at the plant, said his members are increasingly concerned: "In my experience once these jobs go they never come back.
"And that's why we have to do everything possible to keep these jobs in the area."
A government spokesperson said: "We have put forward a precise and credible plan for our future relationship with the EU.
"As part of this we have proposed a UK-EU free trade area underpinned by a common rulebook on manufactured goods, such as automotives."
Toyota at Burnaston
Started production December 1992
Employs 2,564 (inc 322 agency)
Produces Auris and Avensis - including pressing body panels, welding and assembly
Site is 580 acres - 2.35 million square metres
Total vehicles produced: 144,077, of which Avensis: 25,057, Auris: 34,899 and Auris Hybrid: 84,121