He suffered the injury during today's training run.
Clarke is having scans to establish the extent of the injury and his likely return to play, however he has been ruled out of the remainder of three-test series against France.
The final test is next weekend in Hamilton. The All Blacks lead the series 1-0 following their 31-27 win in the first match in Dunedin.
Clarke has been replaced in Saturday's matchday 23 by Emoni Narawa.
Narawa, who was initially named in the squad as injury cover, comes on to the right wing, with Rieko Ioane, originally picked in the No 14 jersey, switching back to the left wing, where he started in last weekend's win in Dunedin.
It is disappointing for Clarke, who missed selection in the opening test against France and was looking to cement himself in the All Blacks starting side after a tough Super Rugby season for the Blues, in which he failed to score a try.
Saturday's test between the All Blacks and France is part of a double header in Wellington which kicks off with the O'Reilly Cup clash between the Black Ferns and Wallaroos.
All Blacks team to play France
Will Jordan, Emoni Narawa, Billy Proctor, Jordie Barrett, Rieko Ioane, Beauden Barrett, Cam Roigard, Christian Lio-Willie, Ardie Savea (c), Tupou Vaa'i, Fabian Holland, Patrick Tuipulotu, Fletcher Newell, Codie Taylor, Ethan de Groot. Reserves: Samisoni Taukei'aho, Ollie Norris, Pasilio Tosi, Samipeni Finau, Du'Plessis Kirifi, Cortez Ratima, Timoci Tavatavanawai, Damian McKenzie.
