Ledley has missed the past two matches with a groin injury, and Lennon hopes the problem will be cured by a month's rest.
The manager said: "Joe will not be back until mid-January when the winter break ends. He is having rest to settle the injury down."
Ledley's next appearance is likely to come against Hearts on 19 January, and in the meantime the champions take on Ross County, Dundee, Hibernian and Motherwell.
Kris Commons (thigh) will miss the first of those games, but James Forrest could return from a hamstring injury.
Don't miss any live and exclusive football coverage this festive season. Click here to visit Sky Sports' Festive Calendar