Flanker Cane, who made his debut against Ireland in 2012, impressed as a replacement during the All Blacks' hard-fought 26-16 victory over Argentina in their opening Pool C clash.
Cane is rewarded with the armband after Steve Hansen made 12 changes to the starting XV for the next clash at London's Olympic Stadium, with only Sam Whitelock, Julian Savea and Nehe Milner-Skudder retained from the previous line-up.
Codie Taylor, Luke Romano, Liam Messam, Tawera Kerr-Barlow and Malakai Fekitoa are set to make their first World Cup appearances.
"It's a very special moment for 23-year-old Sam Cane who will captain the All Blacks for the first time," Hansen told the All Blacks' official website.
"He's in our leadership group, is hugely respected by everyone, is a fierce and fearless player and is someone who has the potential of being a long-term captain of the All Blacks in the future.
"Five of our team will also be playing their first Rugby World Cup match so it'll be a significant moment for them and their families as well."
All Blacks: Colin Slade, Nehe Milner-Skudder, Malakai Fekitoa, Sonny Bill Williams, Julian Savea, Beauden Barrett, T J Perenara; Ben Franks, Codie Taylor, Charlie Faumuina, Luke Romano, Samuel Whitelock, Liam Messam, Sam Cane (c), Victor Vito
Reserves: Keven Mealamu, Wyatt Crockett, Tony Woodcock, Kieran Read, Richie McCaw, Tawera Kerr-Barlow, Ma'a Nonu, Ben Smith