Jaguar Land Rover workers at the company’s Solihull plant have been put on a three-day week until Christmas.
The UK’s largest carmaker said it was making “temporary adjustments to our production schedules” at its Castle Bromwich factory.
Jack Dromey, the Labour MP for Erdington, blamed the “Brexit chaos and the mishandling by ministers of the transition from diesel” for the move.
He said the change was intended to prevent further job losses at JLR.
Both issues were a “growing threat” to the plant, Mr Dromey tweeted.
JLR said in a statement it was standard business practice to “regularly reviews its production schedules to ensure market demand is balanced globally”.
“In light of the continuing headwinds impacting the car industry, we are making some temporary adjustments to our production schedules at Castle Bromwich,” the carmaker said.
“We are however continuing to over-proportionally invest in new products and technologies and are committed to our UK plants in which we have invested more than £4 billion since 2010 to future proof manufacturing technologies to deliver new models.”
Last week, JLR boss Ralf Speth warned the government to get “the right Brexit” or risk big job cuts at the carmaker.
The production cutbacks come on the day that Sir Bernard Jenkin, the Tory MP and Brexit supporter, accused Mr Speth of scaremongering with his prediction.
“I’m afraid I think he’s making it up. We’ve had figures made up all the time by the scaremongers in this debate and I’m afraid nobody believes them,” he told the BBC’s Today programme.
Sir Bernard’s comments were described as “embarrassing” by pro-Remain Tory backbencher Anna Soubry.