Coles was substituted 24 minutes into Saturday's Test in Paris, which ended in a 38-18 victory for the All Blacks.
The Hurricanes man had opened the scoring for Steve Hansen's side but will play no further part in their Northern Hemisphere tour.
The injury requires surgery and carries a recovery period of four to six months.
New Zealand have also confirmed the team that will take on a France XV in Lyon on Tuesday, with six players set to make their first appearance for the All Blacks.
Jack Goodhue, Atu Moli, Akira Ioane, Dillon Hunt, Mitch Drummond and Richie Mo'unga are included, alongside Tim Perry, Matt Duffie and Asafo Aumua, who are yet to play in a full Test fixture for their country.
The side will be captained by Luke Whitelock, with Ardie Savea, Tawera Kerr-Barlow and Lima Sopoaga among the men adding some senior-squad experience.
"Whilst Luke Whitelock is only playing his second game for the All Blacks, he was an obvious choice as captain given his experience and leadership as captain of both the Highlanders and Canterbury Mitre 10 Cup team," said Hansen.
"This match was included in the Vista Northern Tour itinerary at our request to allow us to provide an extra opportunity for this group. It'll allow us to continue to grow our depth, which will not only bode well for the here and now, but also 2019 and well beyond.
"This group has trained well and we're looking forward to watching them play at this level."
Francois Trinh-Duc, who has 61 Test caps to his name, is the most recognisable face in an unfamiliar French starting line-up.
France: Scott Spedding, Gabriel Lacroix, Henry Chavancy, Jonathan Danty, Hugo Bonneval, Francois Trinh-Duc, Yann Lescourgues; Dany Priso, Chat, Malik Hamadache, Romain Taofifenua, Yoann Maestri (c), Wenceslas Lauret, Sekou Macalou, Marco Tauleigne.
Replacements: Christopher Tolofua, Mohamed Boughanmi, Lucas Pointud, Julien Le Devedec, Fabien Sanconnie, Maxime Machenaud, Jules Plisson, Vincent Rattez
New Zealand: David Havili, Matt Duffie, Jack Goodhue, Ngani Laumape, Seta Tamanivalu, Lima Sopoaga, Tawera Kerr-Barlow; Tim Perry, Nathan Harris, Jeffery Toomaga-Allen, Patrick Tuipulotu, Dominic Bird, Liam Squire, Ardie Savea, Luke Whitelock (c).
Replacements: Asafo Aumua, Atu Moli, Ofa Tu'ungafasi, Scott Barrett, Akira Ioane, Dillon Hunt, Mitch Drummond, Richie Mo'unga.
Photo Getty Images. Caption: All Blacks Dane Coles