St Ledger has been sidelined since suffering the injury during the 2-0 home win over Bristol City on October 6.
The Republic of Ireland international was expected to be back playing before now, but the problem has proven to be more complex than initially thought.
He is currently in Munich in a bid to get to the bottom of the injury, which may even require surgery.
"Sean is in Munich now," confirmed Leicester manager Nigel Pearson in his pre-match press conference ahead of his side's Championship clash with league leaders Cardiff on Saturday.
"He is going to be a while yet but, hopefully, we will get some positive news in the new year."