The Senegal international suffered the injury in last month's 2-1 defeat to Swansea.
He travelled to Paris for the operation on Thursday and is expected to be out 'for a number of months' according to the Premier League club.
The 28-year-old will begin his rehabilitation at the Clairefontaine medical centre before returning to Tyneside.
Manager Alan Pardew, who does not expect the forward to return inside four months, said: "We are so disappointed for him and for us. He always, always gives 100 per cent for us.
"He's not had the greatest of seasons, so it's a real blow for him because I am sure he is determined next season to show what he did two years ago when he couldn't stop scoring, so our thoughts are with him."
The news will come as a huge blow for Cisse, who would have been hoping to hit the ground running next term 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 and has netted just twice in the Premier League this season.