Ford Motor Co. expects to lay off several thousand workers temporarily at a Michigan factory that assembles its top-selling F-150 pickup truck after a fire last week damaged the premises of a parts supplier, people familiar with the matter said.

The blaze, which occurred Wednesday at a Michigan plant operated by Meridian Lightweight Technologies, has already disrupted production of Ford’s pickup trucks at a factory in Missouri. Meridian is an automotive-interiors supplier owned by China’s Wanfeng Auto Holding Group, which...