The Czech Republic international dislocated his shoulder in the UEFA Champions League semi-final first leg draw against Atletico Madrid on April 22.
In a statement on their website, Chelsea confirmed Cech would be "out for approximately eight to 10 weeks" after his operation.
The 31-year-old, whose nation failed to qualify for the FIFA World Cup, will miss very little - if any - of Chelsea's pre-season.
Ruled out for the rest of the campaign when the injury occurred, Cech will be sidelined for Chelsea's final Premier League match of the campaign - a trip to Cardiff City on Sunday.
Australian veteran Mark Schwarzer has deputised in his absence.
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