The France international has been out of action since the Toffees' defeat at Aston Villa four weeks ago.
The club hoped the 32-year-old would be back in action within a month but he has not recovered as quickly as expected.
David Moyes said: "He goes to a facility in France to get treatment and looked after and I think it will be two to three weeks before he is available."
In a further blow for Moyes, forward Victor Anichebe has been forced to undergo surgery to repair a troublesome knee injury.
The 22-year-old has not featured this season due to the problem and has now been told an operation is necessary.
Moyes said: "He had an operation yesterday which will keep him out for six weeks or so."
Source: Team Talk
Source: Team Talk