The impact of the ongoing strike by auto workers at General Motors (GM) - Get Report in the U.S. is being felt across the northern border as thousands of Canadian auto industry workers have been furloughed and more temporary layoffs are coming.

About 4,500 members of Canadian trade union Unifor, which represents GM and other auto workers in Canada, have been temporarily laid off because of the strike so far, union President Jerry Dias told CNBC. He said that includes about 2,500 workers at GM's Oshawa Assembly plant and 2,000 people who work for GM's suppliers. He said non-unionized plants are being impacted as well.

A GM Canada spokeswoman said in an email to TheStreet that the majority of its 7,600-member workforce in Canada hasn't been impacted, "however I can confirm that approximately 2,000 workers are on temporary layoff due to a parts shortage related to the UAW strike and we expect to resume production in Oshawa upon resolution." The spokeswoman said stamping operations in Oshawa and production at GM Canada's operations in Ingersoll and St. Catharines continue.

A Unifor spokesperson told TheStreet that about 700 workers at the company's plant in St. Catharines, Ontario, are expected to be temporarily laid off on Monday, or about two-thirds of the workforce there. The spokeswoman said the Cami plant in Ingersoll is still running at full capacity but the operations will be re-evaluated at the end of next week.

About 48,000 members of the United Auto Workers union that work at GM in the U.S. have been on strike since Monday after the two sides failed to agree on a new contract. It is the union's first national strike against the automaker since a two-day work stoppage in 2007. It's unknown how many workers at suppliers in the U.S. have been impacted by the strike.

Dias told CNBC that the Canadian union members support the UAW's strike against GM, despite the impact on their jobs.