The 44-year-old helmer posted the photograph on Instgram captioned as, "#Davos #worldeconomicforum #georgeclooney".
Karan flew to Switzerland for the five-day conference, after releasing his autobiography, "An Unsuitable Boy".
Clooney, 55, was in Davos with his wife Amal, who was felicitated for her extrordinary contribution in the field of global human rights.
Karan had said earlier that he was looking forward to this novel experience on being invited as a cultural leader at WEF this year.