The company disclosed in December that Blake had been diagnosed with lymphoma, which Blake said at the time was "treatable." He had expected to work through his illness.
It could not be immediately determined whether the lymphoma was the cause of Blake's death.
Michael Dart, a partner at consulting firm A.T. Kearney who worked with Blake, described him as genuine, caring, authentic and thoughtful.
"He was incredibly generous with his time, even when he was fighting his illness. A true inspiration," Dart said.
Nordstrom said on Wednesday that Blake's brothers, Pete and Erik Nordstrom, will continue on as co-presidents of the company.
The brothers' great-grandfather, Swedish immigrant John Nordstrom, founded the company, which started as Wallin & Nordstrom, in 1901.
Since then, the retailer has evolved into one of the country's most renowned department stores, known for its customer service and a luxury price-point more affordable than peers like Neiman Marcus.
It has also has weathered retail upheaval. Blake, along with his brothers, explored taking the retailer private in 2017, but called off those on-and-off efforts last year. The family and the special committee advising Nordstrom's board were unable to agree on a price amid a challenging financing market.
Since then, the company has focused on what Blake said in the company's November earnings call was its aspiration of being "best fashion retailer in a digital world." Nordstrom was one of the earliest department stores to make a bet on e-commerce, a move that many say has helped it stay ahead of peers. It acquired HauteLook, a members-only shopping website, in 2011. Last year it acquired digital retail start-ups BevyUp and MessageYes to further its digital efforts.