The photo shows Ontario resident Elfriede Wolf firmly clasping Mr Clooney's hand while cupping his chiselled chin and looking into his eyes.
Ms Wolf tells Canada's Global News her daughter Brigitte is "in love" with the heartthrob. So, as the actor walked past her, she decided to yell out, "George, my daughter is in love with you."
Ms Wolf says a startled Mr Clooney replied with an "Oh my God."
He then smiled and reached over to clasp her hand. That's when she grabbed his chin.
"He is very handsome," she tells the BBC. "It was over in a moment, I was just so, so taken by that."
"That's adorable," tweeted one person. "Even George knows real Nonnas squeeze faces! Good for both of them," tweeted another.
On Reddit, people had plenty of fun with the viral photo. Take a look:
Mr Clooney was at the film festival to promote his latest film, Suburbicon. Click for more trending news