"This is a tragedy too big to be written," Astana said in a statement, paying tribute to the 37-year-old, who won the Giro d'Italia in 2011.
"Ciao Michele," Astana wrote on Twitter.
The fatal crash happened on a crossroad near his home in central Italy and he leaves behind a wife and two children, Astana said.
Citing police sources, the Italian daily Il Resto del Carlino said that the driver of the vehicle "did not see" Scarponi.
More From This Section
He outsprinted Briton Geraint Thomas and Thibaut Pinot of France to claim the early lead of the race, a key warm-up event ahead of next month's Giro d'Italia, the first of the year's Grand Tours.
Scarponi was gearing up for another tilt at the Giro, which starts on May 5 in Sardinia, when the collision occurred in Filottrano, in Ancona province.
"Immense tragedy. There are no words. Rest in peace my friend," Aru tweeted.
Scarponi won the 2011 Giro after Alberto Contador was stripped of the title for doping. The Italian was himself suspended for doping for 18 months between 2007 and 2008.
Contador was among the first to express his shock, tweeting that he was "paralysed and speechless".
He described Scarponi as "a great person and always with a contagious smile".
Astana said Scarponi had gone home after finishing fourth on Friday in the Tour of the Alps and spent the evening with his young family.
"We left a great champion and a special guy, always smiling in every situation, he was a real milestone and a landmark for everyone in the Astana Pro Team," it said.
"The Astana Pro Team clings to the Michele family in this incredibly painful moment of sorrow and mourning."
Other cycling teams expressed their sadness.
"Our thoughts and prayers go to the family, friends and team of Michele Scarponi, who passed away this morning in a traffic incident," Quick-Step Cycling team said on Twitter.
Scarponi's death underlines the dangers faced by professional cyclists training on the roads.
In January 2016 six riders from the Giant-Alpecin team, including Frenchman Warren Barguil and John Degenkolb of Germany, were seriously injured after being hit by a car during a training trip to Spain.
Two months later Frenchman Romain Guyot, a young cyclist with the Vendee U team, died after being struck on his bike.