The French defender was forced off with a hamstring injury at half-time of Sunday's victory over Manchester United and will definitely miss Saturday's trip to Southampton.
By the weekend Everton hope to be in a position to know the extent of the injury but the worst-case scenario is the season is over for the 36-year-old, who up until the weekend had completed 90 minutes in every one of his previous 31 league starts.
"Sylvain had to come off against United on Sunday and he won't be fit for this weekend," said manager Roberto Martinez.
"It is a little bit too early to know how long he is going to be out.
"I do think that over the next 48 hours we will have a clear idea of whether he will be available before the season ends."
With Phil Jagielka still not ready to return from a hamstring injury which has sidelined him since the end of February it leaves Martinez with youngster John Stones, who has impressed deputising for Jagielka, and Antolin Alcaraz - who has played just five times since making his debut in December following an injury-troubled start to life at Goodison Park following after his summer move from Wigan.
Jagielka is expected to return next weekend when title-chasers Manchester City visit.
Midfielders Steven Pienaar and Darron Gibson (both knee), strikers Arouna Kone (knee) and on-loan Lacina Traore (hamstring) and defender Bryan Oviedo (broken leg) are all still sidelined.
Source : PA
Source: PA