The 57-year-old had been heading to a film set on Tuesday when his motorbike was hit by a vehicle, according to local daily La Nuova Sardegna. The accident occurred at Costa Corallina, on a country road.
A picture from La Nuova shows a smashed windscreen, which suggests George hit it during the crash, but despite this, his condition is not thought to be serious.
"A vehicle did not respect the right of way and hit him", the tweet read.
Clooney is now on the island filming a new TV series "Catch-22", based off the book of the same name written by Joseph Heller.
He was joined by wife Amal Clooney and it has been reported that the pair left the hospital together in a private vehicle.
How rescuers plan to get trapped boys out of Thai cave
Rescuing them all could take three to four days and depended on the weather, an army commander involved in the mission said. The operation was launched at 10 am local time (0400 CET) on Sunday and involves 13 foreign divers and 5 Thai navy SEALs.
George has been working hard in the region for his new project Catch 22, with the star directing, producing and starring in the six episode miniseries based on Joseph Heller's seminal novel.
Set in Italy during World War II, Catch-22, follows the story of the artful dodger Yossarian, a bombardier for the US Air Force, who is furious because many others he has never met are trying to kill him.
Clooney was pictured stepping off a private jet with wife Amal and twins, Alexander and Ella, near the end of last month. It's unclear when George will return to filming.
Clooney has a home on the Italian mainland, on Lake Como.