Franks, who had already been ruled out of the Rugby Championship, will now also miss the end-of-year tour after deciding to undergo surgery on Friday.
The All Blacks and Crusaders had been managing Franks' problem all year, but he was a late withdrawal from the second Bledisloe test after the injury became more serious.
"It's better to get it right and let him have a full recovery and a pre-season and get back for the Crusaders," All Blacks coach Steve Hansen said today.
The All Blacks will also be without Waisake Naholo for this weekend's clash against Argentina, the Taranaki winger ruled out due to a concussion sustained against Counties Manukau.
Auckland flanker Blake Gibson has been called into the squad, as Hansen wants to have a closer look at the 22-year-old within the All Blacks environment.
Ryan Crotty, Sam Cane and Wyatt Crockett have all overcome their respective ailments to be fit to play on Saturday night.
While Cane is available to play the Pumas on Saturday, Gibson's inclusion is significant because it gives an indication of the selectors' thinking in terms of a succession plan.
Matt Todd would have been next in line but has fractured a hand, and Hansen says Otago pair James Lentjies and Dillon Hunt are also in the mix.
"With Matt Todd getting injured it created a thought process of 'gee whizz, who is next?'," Hansen said.
"It came down to Blake and the two Otago boys Lentjies and Hunt, and we just felt let's have a look at Blake this week and get some better information on him. You can watch as many games as you like but having him in your training environment is good and in the next wee while we'll probably have a look at the other two as well.
"[Blake] is good over the ball - he's a strong, physical player, his history in the game is pretty good. He's a New Zealand under-20 player with a lot of talent and has done a good job, although he's copped a few injuries, with the Blues and Auckland."
Hansen hinted at making changes to his line-up for the test at Yarrow Stadium.
"It's a fine line. On one hand you're looking to grow your squad. On the other hand you're trying to grow combinations. If you chuck in all the travelling as well - it's a lot of travelling. Whatever we do it will cause some conversations so that will be good for the game. The expectation will be that we will field a very good side and we'll go from there. It doesn't matter who plays, the expectation is we will do well."