The skipper was forced to hobble off after 66 minutes of the 2-0 win against the Blues and although reports after the game suggested it wasn't too serious, he hasn't managed to recover in time for the trip to the Hawthorns.
Noe Pamarot replaced Ledley on Boxing Day and Head Coach Martin Jol looks set to choose between the Frenchman and Anthony Gardner, who is added to the squad.
Anthony partnered Michael Dawson in central defence for the first four games of the season when Ledley was ruled out by injury.
Ledley has lined-up with Michael in the last 10 games and the defensive unit - also including Paul Robinson, Lee Young-Pyo and Paul Stalteri - have remained unchanged in that time.
Teemu Tainio remains a doubt with a knee problem and Andy Reid is out for a month with a knee ligament injury.
Ledley King is out of Wednesday night's clash at West Brom with the groin injury he picked up against Birmingham on Boxing Day.