The All Blacks on Monday gave updates on 10 players, including the inspirational No.8, who were injured during the four-Test series against the Springboks, which New Zealand lost 3-1.
The statement said the timeline for Savea's return to play would be determined after the operation.
Surgery on a dislocated shoulder normally requires four to six months recuperation, which would also rule Savea out of the second half of the Nations Championship in November.
His fellow loose forward Luke Jacobson will be sidelined for four to five months by an elbow tendon injury, ruling him out for the rest of the season.
Winger Caleb Clarke has also played his last match this year with a ruptured shoulder tendon keeping him out for five months, while prop Ollie Norris is slated to return from a knee cartilage injury in time for the Super Rugby pre-season.
Anton Lienert-Brown, who suffered a knee injury, will return in four to six weeks, a similar recovery period to his fellow centre Billy Proctor, who fractured a shoulder blade.
A third centre, Quinn Tupaea, could face the Wallabies after being listed as one to two weeks away from recovery from his knee issue.
Flanker Anton Segner (ankle-joint inflammation) will also be back in a couple of weeks, while hooker George Bell, who was sent home from South Africa with a calf injury, scored a hat-trick of tries for Canterbury in the National Provincial Championship on Sunday.
New Zealand host Australia in Auckland on October 10 with the return match in Sydney the following week. Australia relinquished the Bledisloe Cup in 2003 and the All Blacks have held it since.
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