The 35-year-old, who won the 2006 MotoGP world title, suffered severe chest and head injuries in the accident, which happened while he was training on his bicycle in central Italy, south of the seaside resort of Rimini.
Hayden, nicknamed "The Kentucky Kid", raced in MotoGP from 2003 to 2015 before moving to the Superbike World Championship for the 2016 season.
He won just three races in MotoGP – all in the 2005-06 season – but he famously took the world title that season after fighting tooth-and-nail with Valentino Rossi's Yamaha.
His death comes exactly a month after veteran Italian professional cyclist Michele Scarponi was killed after being hit by a van while out on a training ride on roads near his home.
Honda teammate Stefan Bradl said he was “deeply touched and saddened”.
Current Honda MotoGP rider Dani Pedrosa, who was Hayden’s teammate in 2006, posted a photo on twitter of the American along with the words “Always in my heart, champ. RIP Nicky. #69.”