The defender picked up the issue during the Reds’ friendly with Borussia Dortmund in Notre Dame on Friday.
He has not travelled with his teammates to New York for the final stop on the club’s United States tour and has instead returned to Melwood to begin his rehabilitation programme.
Jürgen Klopp told Liverpoolfc.com: “What can I say other than how gutted we all are for Clyney. He was training and playing so well - he was in outstanding shape.
“Clearly an injury of this nature isn’t a happy moment for any player, but the silver lining for him is that, according to the medical guys, it’s a straightforward ACL injury.