The 30-year-old suffered the problem in the 2-1 win at Goodison Park.
It enabled back-up keeper Ross Turnbull to step in for Wednesday's 1-0 home defeat by QPR in only his fifth Premier League game for the Blues.
In a club tweet, manager Rafa Benitez provided a medical update on Cech, saying: "Two or three weeks. We are quite optimistic."
The news will not be welcome at Stamford Bridge after the loss to the league's bottom side meant the gap on leaders Manchester United remained at 14 points, although Chelsea have a game in hand.
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