Hayden won the MotoGP title in 2006, finishing narrowly ahead of Italian great Valentino Rossi.
In a MotoGP career spanning 2003-16 with Honda and Ducati, Hayden posted three victories and 28 podium finishes in 218 races.
After switching to the World Superbike championship last year, Hayden finished fifth overall.
Hayden was 13th in Superbike this season, riding for the Red Bull Honda team.
Fellow motorcycle racers reacted to Hayden's death on Twitter.
"I'm shattered after the news. We will never forget you!" wrote three-time MotoGP world champion Marc Marquez.
"Always in my heart, champ. RIP Nicky. #69," wrote MotoGP standout Dani Pedrosa.
Hayden was born in Owensboro, Kentucky.
Several family members had flown in from the United States, including Hayden's mother and brother.