Around 1,000 workers at Jaguar Land Rover's Castle Bromwich factory are going to a three-day working week.
JLR said a cut in production is due to "continuing headwinds" affecting the car industry.
Sales of Jaguar models are down by almost seven per cent this year.
But the company said it is also a drop in diesel sales and uncertainty over Brexit - with people holding off buying new cars - which is hitting the business.
The workers are all based at the JLR's Castle Bromwich factory which makes Jaguar's saloons.
The move came hours after former shadow minister Sir Bernard Jenkin accused JLR chief executive Professor Dr Ralf Speth of scaremongering over a prediction that crashing out of the EU would have a "horrifying" effect on the JLR's business.
Professor Speth - speaking at the UK's first Zero Emission Vehicle Summit in Birmingham last week - said that a 'hard Brexit' could result in the "worst of times" for the UK while the cost to Jaguar Land Rover would be more than £1.2billion a year.