Pietersen, 34, had been due to fly to India on Friday to fulfil his IPL contract with Sunrisers Hyderabad.
He was told he would not be selected for England on Monday, despite making 355 not out for Surrey against Leicestershire.
Media playback is not supported on this device
Pietersen sustained the injuries during that County Championship match, and is expected to be out for two weeks.
The South Africa-born batsman, who has not represented England since he was sacked in February 2014, was bought at the IPL auction by Hyderabad for £205,000 (20m rupees) in February.
However, incoming England and Wales Cricket Board chairman Colin Graves said Pietersen could be in contention for an international recall if he joined an English county and scored enough runs.
As a result, the right-hander pulled out of a deal with Hyderabad and signed for Surrey, although he would still be contracted to play in the later stages of the IPL.
Despite Pietersen's highest score of his career, England's director of cricket Andrew Strauss has again blocked him from returning to the national side because of "massive trust issues".
Pietersen said he was "angry and hurt" at being told he will not be considered for selection by England, accusing the ECB of being "deceitful".
Hyderabad, who sit third in the IPL table, have two group games remaining. The final is held on 24 May.
Batsman Kevin Pietersen will not play in this year's Indian Premier League because of calf and Achilles injuries.