After two years of the pandemic, semiconductor shortages and supply chain chaos, it seemed like nothing else could go wrong for the auto industry and the millions of people it employs. But then came thousands of truckers who, angry about vaccine mandates, have been blocking major border crossings between Canada and the United States.

With Canadian officials baffled about what to do, the main routes that handle the steel, aluminum and other parts that keep car factories running on both sides of the border were essentially shut down Wednesday and Thursday.

Ford Motor, General Motors, Honda and Toyota have curtailed production at several factories in Michigan and Ontario, threatening paychecks and offering a fresh reminder of the fragility of global supply chains and of the deep interdependence of the U.S. and Canadian economies, which exchange $140 million in vehicles and parts every day.

No one knows how this is going to end. The protests are expected to swell in the coming days and could spread, including to the United States. Canada’s transport minister has called the bridge blockades “illegal,” and the government has mobilized the Royal Canadian Mounted Police. The mayor of Windsor, Ontario, has threatened to remove the protesters. But those statements have seemed to have little impact. Gov. Gretchen Whitmer of Michigan pleaded with Canadian officials to quickly reopen traffic.

“They must take all necessary and appropriate steps to immediately and safely reopen traffic so we can continue growing our economy,” Ms. Whitmer said in a statement on Thursday.

The chaos is already starting to take an economic toll. The pain is likely to be most acute for smaller auto parts suppliers, for independent truckers and for workers who get paid based on their production. Many of these groups, unlike large automakers like G.M., Ford and Toyota, lack the clout to raise prices of their goods and services. Companies and workers in Canada are more likely to suffer because they are more dependent on the United States.

The longer crossings between the countries remain blocked, the more severe the damage, not only to the auto industry but also to the communities that depend on manufacturing salaries. Workers at smaller firms typically receive no compensation for lost hours, said Dino Chiodo, the director of auto at the giant Canadian union Unifor. Workers who have been sent home early because of parts shortages will spend less at stores and restaurants.

“People say, ‘I have $200 less this week, what do I do?’” Mr. Chiodo said. “It affects the Canadian and U.S. economy as a whole.”

Auto factories and suppliers in the United States generally keep at least two weeks of raw materials on hand, said Carla Bailo, the president of the Center for Automotive Research in Ann Arbor, Mich. If the bridges remain blocked for longer than that, she said, “then you’re looking at layoffs.”

The blockades came after a demonstration in the Canadian capital of Ottawa that started nearly two weeks ago. The protests began over a mandate that truck drivers coming from the United States be vaccinated against the coronavirus and have grown to include various pandemic restrictions. Some have demanded that Prime Minister Justin Trudeau resign. The truckers have been joined by various groups, including some displaying Nazi symbols and damaging public monuments.

The crossing that has the auto industry and government officials most concerned is the Ambassador Bridge, which connects Windsor and Detroit. It carries roughly a quarter of the trade between the two countries, which has been relatively unrestricted for decades. While food and other products are also affected, about a third of the cargo that uses the bridge is related to the auto industry, Ms. Bailo said.

The blockade has been felt as far south as Kentucky, where production has been disrupted at a Toyota factory, the company said on Thursday. The shutdown at the border also will prevent manufacturing at Toyota’s three Canadian plants for the rest of the week, said Scott Vazin, a company spokesman.

G.M. said it had canceled two shifts on Wednesday and Thursday at a factory in Lansing, Mich., that makes Buick Enclave and Chevrolet Traverse sport utility vehicles. The company also sent workers from the first shift at a plant in Flint, Mich. home early. Ford said Thursday that plants in Oakville and Windsor, both in Ontario, were running at reduced capacity.

Shortages of semiconductors and other components have not been all bad for giant automakers, creating scarcity that has driven up prices of cars in the last year. Ford and G.M. both reported healthy profits for 2021. And the economic damage will not be severe if the bridge and other crossings reopen soon, industry experts said.

But the last two years have shown that, because supply chains are so complex, problems at obscure parts makers can have far-reaching and unpredictable impact. Last year, Ford had to shut down plants for weeks at a time in part because of a fire at a chip factory in Japan.

“If it stretches on for weeks it could be catastrophic,” said Peter Nagle, an analyst who covers the car industry at IHS Markit, a research firm.

Mr. Nagle said the bridge blockade was worse than the semiconductor shortage for carmakers. They “were already running pretty tight because of other supply chain shortages,” he said. “This is just bad news on top of bad news.”

The auto industry operates relatively seamlessly across Canada, the United States and Mexico. Some parts can travel back and forth across borders multiple times as raw materials are processed and are turned into components and, eventually, vehicles.

An engine block, for example, might be cast in Canada, sent to Michigan to be machined for pistons, then sent back to Canada for assembly into a finished motor. The blockades have stranded some truckers on the wrong side of the border, creating a chain reaction of missed deliveries.

The slowdown in Canadian trade will disproportionately impact New York, Michigan and Ohio, said Arthur Wheaton, the director of labor studies at Cornell’s School of Industrial and Labor Relations. At the same time, he added, the protests were “certainly raising concerns for all U.S. manufacturers.”

“There is already a shortage of truck drivers in North America, so protests keeping truckers off their routes exacerbates problems for an already fragile supply chain,” Mr. Wheaton said.

Carmakers had hoped that shortages of computer chips and other components would ease this year, allowing them to concentrate on a long-term threat: the transition to electric vehicles. But the chances of a return to normal recede the longer the blockades last.

A larger fear for many elected officials and business executives is that the scene at the Ambassador Bridge could inspire other protests. The Department of Homeland Security warned in an internal memo that a convoy of protesting truckers was planning to travel from California to Washington, D.C., potentially disrupting the Super Bowl and President Biden’s State of the Union address on March 1.

“While there are currently no indications of planned violence,” the memo, which was dated Tuesday, said, “if hundreds of trucks converge in a major metropolitan city, the potential exists to severely disrupt transportation, federal government operations, commercial facilities and emergency services through gridlock and potential counter protests.”

Mr. Chiodo, the Canadian union leader, said that “the people who are demonstrating are doing it for the wrong reasons. They want to get back to the way things were before the pandemic, and in reality they are shutting things down.”

Dan Bilefsky, Neal E. Boudette and Zolan Kanno-Youngs contributed reporting.