Amal Clooney reportedly rushed to his side while he was at the hospital.
The A-list couple are believed to have brought their parents to the Italian island to help care for the children while Clooney works.
Clooney, 57, was reportedly thrown from his two-wheeler on to the windscreen of the vehicle in Costa Corallina on the island's northeast coast at around 8 am. The actor's helmet struck the car's windshield, causing it to shatter and the helmet to break.
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Wife Amal, 40, came to collect him and the couple left in a chauffeur-driven vehicle.
The star who lives in Sonning, Berkshire with his wife Amal Clooney and their two children, doesn't appear to be badly injured.
His rep confirmed the accident to "Extra", saying, "George was treated and released from an Olbia hospital".
Catch 22 was written by Luke Davies and David Michôd and is based on the Joseph Heller novel with the same title.
"Catch-22" is slated to air next year.