Small businesses and shipping firms are preparing for a possible Canada Post strike as early as next week, a disruption they warn could strain supply chains and freeze millions of packages as well as billions of dollars in sales.

While the Canadian Union of Postal Workers and the postal service had been in talks since April 30, Canada Post said late Tuesday that it was hitting pause on negotiations after it said days of trying to hash out a deal had gone by "without meaningful progress."

The post…