The defender, who hasn’t figured for the Reds this season due to the injury, underwent the procedure on Monday.
Clyne will now begin a rehabilitation programme with the club’s medical team.
There were no complications with the operation.
The 26-year-old is in good condition due to the extensive treatment he has already undergone in the first part of this campaign.
This means Clyne is on course to return to action in the new year and be available for selection once more for Liverpool, though no specific time frame has been placed on his return.
His last appearance for the Reds came during the second 45 minutes of the first pre-season friendly of the summer against Tranmere Rovers at Prenton Park on July 12.