Neesham, who was bought at this year's auction, and Lynn, who was retained from last year, were both been ruled out based on the injury reports received from their respective boards, said a release from the Board of Control for Cricket in India on Tuesday.
The IPL regulations permit replacement if a player is unavailable for the entire season.
Kolkata opted to replace the injured players with the experienced duo of Azhar Mahmood, former Pakistan Test cricketer who is currently based in England playing for Surrey, and former South Africa off-spinner Johan Botha.
KKR will take on Mumbai Indians in the opening encounter on April 8.
Image: Azhar Mahmood in action for Kings XI Punjab during the sixth edition of IPL in 2013.
Photograph: BCCI