Pozzovivo was involved in the collision while training near Cosenza in southern Italy.
The 36-year-old was taken to a local hospital and remains in intensive care.
"Although stable and conscious (Pozzovivo) has suffered multiple bone fractures requiring surgery," the team said.
"@pozzovivod suffered fractured arm and leg after being hit by a car," they tweeted.
A climbing specialist Pozzovivo helped teammate Vincenzo Nibali to a second-place finish in this year's Giro Italia.
He had been training for the Vuelta a Espana which starts on August 24, but will now likely miss the race with reports suggesting he has suffered further fractures including six broken ribs as well as chest injuries.