The Halewood plant on Merseyside will also have a "limited period of non-production" from Monday.
JLR said that its giant engine manufacturing centre at the i54 to the north of Wolvehampton was currently not affected by the problem and production there would continue next week.
The Jaguar XE, XF and F-Type sports car are built at Castle Bromwich, with Halewood making the Discovery Sport and Range Rover Evoque.
JLR said in a statement: "Like other automotive manufacturers, we are currently experiencing some Covid-19 supply chain disruption, including the global availability of semi-conductors, which is having an impact on our production schedules and our ability to meet global demand for some of our vehicles.
"As a result, we have adjusted production schedules for certain vehicles which means that our Castle Bromwich and Halewood manufacturing plants will be operating a limited period of non-production from Monday, April 26. Manufacturing continues at our Solihull plant.
"We are working closely with affected suppliers to resolve the issues and minimise the impact on customer orders wherever possible."
JLR sales suffered a fall of 13.6 per cent in the year to the end of March due to the impact of the Covid-19 pandemic to 439,588.
The difficulties at the luxury car maker follow similar problems at other manufacturers, including Ford, who have been hit by a global shortage of chips.
A mixture of strong demand and Covid shutdowns at chip makers has also hit mobile phone, TV and video games companies.
The pandemic has also driven up demand for semiconductor chips for use in electronics such as computers, as people worked from home, and suppliers are struggling to adjust.