Chahar sustained the injury days after the auction and missed the subsequent series against Sri Lanka while rehabilitating at the NCA.
There were suggestions that the India seamer would return to action for CSK at the end of April but the setback put paid to all those hopes.
In Chahar's absence, CSK lost each of their first four games this season - a first for the franchise. The franchise will be allowed an injury replacement, a decision on which remains to be made.