Toyota UK has told the BBC a no-deal Brexit would temporarily halt output at its plant in Burnaston, near Derby.
The Japanese carmaker is one of the biggest in the UK and Burnaston produced nearly 150,000 cars last year, 90% for export to the European Union.
Its just-in-time production relies on components imported from the EU.
A spokesperson for the UK government said it is still “confident of securing a good deal”.
Toyota says it cannot predict how long a stoppage would last, but unions fear that if long-term damage is inflicted it could result in job losses.
The Burnaston plant produces the Auris, the UK’s fourth best-selling car, and the Avensis.
Toyota is investing £250m there to enable the production of the new Corolla from the end of this year.
It is taking on 400 new staff, in addition to the 2,500 currently employed there.
“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, managing director at Burnaston.