Papé had hoped to make it back before the end of the season, having suffered the knock in the opening game of the RBS 6 Nations against Italy.
In his absence Thierry Dusautoir took the captaincy, but Papé was expected to play a major role in the three-Test series against the All Blacks.
One player who should be available in New Zealand is scrum-half Maxime Machenaud, who will start for Racing-Metro in their Top 14 play-off clash with Toulouse.
They will be looking to stop the defending champions reaching the semi-finals for the 20th straight occasion and Machenaud admits his team enter the game as underdogs.
He said: "This the first time I've played in the knockout stages. The only ones I've played in were when I was a youngster and I lost every game. I can't wait for the game.
"Toulouse are very solid and have caused us problems but we will try to use our two defeats against them to beat them.
"No one expects us to win so we will try to defy the predictions."