The 30-year-old picked up the knock at Euro 2012 this summer, and Krejci has revealed the details of the strain.
"An investigation showed a bit of ossification in his elbow, so they (Chelsea) are planning a surgery in England after the season," Krejci told CTK.
"They have very kindly asked us if we could rest him in friendly fixtures. We have come to an agreement with coach Michal Bilek and decided to be on good terms with Chelsea. We are going to grant their wish and rest him."
"Petr cannot stretch the arm properly. If he has to stretch the elbow, it hurts him sometimes. There is nothing to be worried about, though. There is basically nothing that could make this problem worse.
"The only thing that could force an immediate surgery is if the intensity of pain would get much higher or if the elbow was blocked in some way."
Cech has started all four of Chelsea's competitive matches this season.