The 57-year-old actor, who is now filming a TV series on the Italian island, was understood to be driving to set when the incident occurred.
Local daily La Nuova Sardegna reports Clooney's injuries aren't serious, but that he was taken to the John Paul II hospital emergency room.
A photo from the Italian website La Nuova showed the car's windshield cracked.
AGI said part of the road was closed following the incident.
Clooney is now filming TV drama Catch-22 on the Italian island.
Federation Internationale de Football Association acknowledges World Cup fever in Bangladesh
When captain Igor Akinfeev and talisman Artem Dzyuba were handed the microphone to address the fans, all of Vorobyovy Gory was drowned out in applause.
This is a developing story and will be updated when more information becomes available.
The couple had previously been enjoying their European trip alongside George's parents Nina and Nick Clooney, as well as Amal's mother Baria Alamuddin.
George and Amal met back in 2013 when Amal attended a party at the Ocean's Eleven star's house in Lake Como, Italy.
The US actor is directing, producing and starring in the six episode miniseries based on Joseph Heller's famous novel. The series is being produced for Hulu.
Hugh Laurie also stars as Major de Coverley for the series which has a release date of 2019.