Automobile and auto-parts manufacturing makes up about 4 percent of the U.S. economy.

G.M., Ford and Fiat Chrysler have all restricted domestic and international travel and told office workers to work remotely.

G.M. has reported one coronavirus infection in its work force, at its technical center in Warren, Mich. The company said it had a medical team assisting the employee’s family and had told others who have been in contact with the affected employee to isolate themselves for 14 days.

“The health and safety of our employees is our top priority,” the company said in a statement.

Ford, G.M. and Fiat Chrysler have all told office workers to work remotely.

Workers at a Ford truck plant in Dearborn, Mich., filed a written grievance against the company on Monday, calling for a shutdown of U.S. factories.

“There’s a lot of concern, just like all across the nation,” said Todd Dunn, president of U.A.W. Local 862, which represents workers at two Ford truck plants in Kentucky. He said many members of his local were scrambling to be able to get to work because day care centers in Kentucky had been ordered closed.

Mr. Dunn said he and his members worried both about the spread of the virus and about the prospect of losing income. “People still have to pay their mortgages,” he said.

On Tuesday, Ford joined Daimler, Nissan, Volkswagen and other major carmakers in shutting down manufacturing operations in Europe.

Ford said the suspension would take effect Thursday and last “for a number of weeks” depending on the spread of the pandemic, as well as disruptions to supply chains, government restrictions on travel, and declines in sales.

Jack Ewing contributed reporting.

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