Clyne is yet to feature for the Reds this season after suffering a back injury during a preseason game against Tranmere.
He did resume light training in September, but the 26-year-old has since suffered a setback and has now undergone "minor, corrective surgery" in a bid to rectify the problem.
The back problem has persisted and the England global recently suffered a setback in his injury comeback.
In a statement, Liverpool said there were "no complications" with the operation. Hot on the heels of returning to action in the 4-1 win over West Ham United, the 25-year played his part as Senegal qualified for their first World Cup in 18-years - an outing that left his long-term fitness in question.
The German gaffer has been forced to rotate Joe Gomez and Trent Alexander-Arnold to fill the void but Liverpool's defence has come under increasing scrutiny.
The former of the pair has performed well in the role when given a chance and was recently called up to the England senior squad.
In a case of "too much, too soon", Liverpool attacker Sadio Mane is on his way back to Merseyside to be assessed by the Reds medical staff after aggravating a hamstring injury that had previously kept him sidelined for a month.
Mané, meanwhile, has been released early from global duty after picking up the problem during Senegal's 2-0 World Cup qualifying win over South Africa last Friday.