Blake Nordstrom, an heir to the Nordstrom Inc. fortune who ran the department-store chain with his two brothers, died unexpectedly Wednesday morning, less than a month after he revealed he had been diagnosed with cancer.

Mr. Nordstrom, 58 years old, was co-president of the retailer, a title he shared with his brothers Erik and Peter. His siblings will continue to lead the company, which is publicly traded but still run and controlled by the family.

“Everyone who worked with Blake knew of his passion and deep commitment to employees, customers and the communities we serve,” said Nordstrom’s board chairman, Brad Smith. A company spokeswoman said Mr. Nordstrom was diagnosed with lymphoma a month ago but couldn’t confirm that was the cause of death.

Mr. Nordstrom, like his brothers, started working at the company at an early age as a stock boy and rose through the ranks. The business was co-founded by their great-grandfather, a Swedish immigrant, more than a century ago. The family turned a single store in Seattle into a company with hundreds of stores across the country and a market value of nearly $8 billion.

The family attempted to take the company private in 2017 but abandoned the effort after they were unable to raise enough financing.