"The world has lost a tremendous visionary and an incredible human being," the statement said. "His spirit will forever be a part of Zappos."
Hsieh was a Harvard University graduate who joined the company — then called ShoeSite.com — in 1999. Zappos was sold to Amazon for $1.2 billion in 2009, but Hsieh had remained with the company until his retirement.
"Tony's kindness and generosity touched the lives of everyone around him, and forever brightened the world," a DTP Companies statement said. "Delivering happiness was always his mantra, so instead of mourning his transition, we ask you to join us in celebrating his life."
For years, Hsieh also worked to revitalize downtown Las Vegas, pledging $350 million in 2013 for redevelopment. The same year he moved Zappos' headquarters into the former Las Vegas City Hall building.
"Tony Hsieh played a pivotal role in helping transform Downtown Las Vegas," Nevada Gov. Steve Sisolak tweeted Friday night. "Kathy and I send our love and condolences to Tony's family and friends during this difficult time."
Many tributes poured out on social media.
"Your curiosity, vision, and relentless focus on customers leave an indelible mark," Jeff Bezos, Amazon's CEO and president, posted on Instagram. "You will be missed by so many, Tony. Rest In Peace."
"Tony Hsieh might be the most original thinker I've ever been friends with," former venture investor Chris Sacca tweeted. "He questioned every assumption and shared everything he learned along the way. He genuinely delighted in making anyone and everyone happy."
Skateboarder and entrepreneur Tony Hawk added, "Tony Hsieh was a visionary. He was generous with his time and willing to share his invaluable expertise with anyone."
"A truly original thinker, a brilliant entrepreneur, and a kind-hearted and generous friend to so many," tweeted entrepreneur Max Levchin.
Ali Partovi, CEO of the venture capital fund Neo, was a partner in one of Hsieh's earliest ventures, the internet advertising company LinkExchange. In a tweet Saturday, Partovi said Hsieh was one of the most creative people he had ever known.
"I'll remember your unique combo of genius and mischief, and your infuriating ability to bet against all odds and win," Partovi said.