The Senegalese forward sustained the injury during Newcastle's 2-1 home defeat by Swansea last month, ending his season, and the 28-year-old travelled to Paris for surgery on Thursday.
A statement on the club's official website said: "He is expected to be sidelined for a number of months."
The news will come as a blow for Cisse, who would have been hoping to hit the ground running next season after a forgettable 2013-14 campaign.
He has often found himself as the third-choice striker behind on-loan QPR forward Loic Remy and Shola Ameobi.
Reduced to cameo roles off the bench, Cisse has netted just twice in the Barclays Premier League this season and appears a shadow of the player that scored 13 goals in his first 14 appearances when he swapped Freiburg for St James' Park in January 2012.
He did net a crucial winner against Crystal Palace in March, but suffered his injury midway through the first half against the Swans.
Cisse will spend his rehabilitation period at the Clairefontaine Medical Centre just outside of Paris before returning to the club to be assessed by medical staff.