Suzuki has suspended production of its Swift models.
Ford has suspended production of its Explorer sports SUV at its Chicago factory.
The European Association of Automotive Suppliers (CLEPA) says some auto component makers have been forced to close plants.
India’s Bajaj Auto said the magnet shortage could start impacting production in July.
There are reports that other Indian car manufacturers – India is the world’s fourth biggest carmaker – will have to stop production soon because of a lack of rare earths.
Indian car makers are reported to have made 20 applications to China for licences to export rare earths to India but none have been approved so far.
Stocks of rare earths at car makers in India are said to vary from three to six weeks so the problems could quickly get worse.