The Wales international will be rested until the Clydesdale Bank Premier League resumes after a short winter break, and could return when Celtic host Hearts on January 19.
Manager Neil Lennon said: "Joe will not be back until mid-January when the winter break ends. He is having rest to settle the injury down."
Ledley will miss the visit of Ross County on Saturday as well as games against Dundee, Hibernian and Motherwell.
Kris Commons remains out against County with a thigh injury but James Forrest might be available following a hamstring problem, which has kept him out since the defeat by Kilmarnock on October 27.
- Sports & Recreation
- Clydesdale Bank Premier League