The Ivory Coast striker will be out for three weeks after undergoing "minimal invasive surgery" on Friday.
It means he will not feature in the Community Shield clash against Manchester United.
And he is a doubt for the Blues' Premier League opener with West Brom a week later on August 14.
A Chelsea statement said: "The decision to perform the procedure after his return from the World Cup was made to optimise his rehabilitation.
"He is expected to return to full training in approximately three weeks."
Like that Chelsea probably will lose Community Shield already :(