Carter was the victim of a crunching tackle by Bismarck du Plessis early in Saturday's Eden Park clash, which the All Blacks won 29-15 to move to the top of the Rugby Championship standings.
The Springboks hooker was controversially shown a yellow card for the tackle by referee Romain Poite and then sent off early in the second half when he received another for lifting his elbow into the throat of flanker Liam Messam.
"We haven't finalised that but it's likely to be Tom Taylor," Hansen told reporters at the team hotel when asked if a replacement for Carter would be needed for the tests in La Plata and Johannesburg.
"Dan has done a grade three AC joint in his shoulder and it looks like he's gone for six weeks. Hopefully he'll be back on the plane for Paris (on the All Blacks' end of season tour)."
It will be Carter's third injury-enforced absence this year after he suffered a broken hand that ruled him out for two games against France in June and then a calf strain that kept him out of the two Rugby Championship games against Australia.
He returned against Argentina last week and Saturday's match at Eden Park was the first time in this season's southern hemisphere competition the All Blacks had the same player at flyhalf for successive tests.
Aaron Cruden played the first match against Australia, then suffered a knee injury that has kept him out since.
Taylor was brought into the squad when third-choice flyhalf Beauden Barrett went down with a calf strain and he made his debut at Wellington Regional Stadium only to suffer a rib injury late in the game that has kept him out of contention.
The 24-year-old so impressed with his composed performance against the Wallabies, injury notwithstanding, he would have been involved in the wider squad even when Carter and Barrett returned to fitness, Hansen said.
"He's shown us what he's more than capable of," Hansen said.
"He deserves to be here. He's got the mental attitude for it. It's tough on Colin (Slade) because he is here (as part of the wider training squad), but Tom would've been here if he hadn't got that rib injury so it's just a swap over."
Hansen said Cruden had taken a full part in training late last week and was likely to be considered for the clash against the Pumas on Sept. 28.
Cruden had also impressed against France earlier this season and then against the Wallabies, though the performance of Barrett on Saturday had people talking about his long-term future in the pivotal role for the All Blacks.
The 22-year-old made a searing break through the middle of the park to set up Brodie Retallick's try, while he was not afraid to run at the Springboks' line and was also sound in the tackle when the visitor's forwards targeted him.
"He was impressive, coming on in that sort of game, that early and playing that position would be tough but he deals with it really well and you can't ask for anything more," centre Conrad Smith said.
"He sometimes doesn't look like he's moving fast but his legs are going," Smith added with a smile of Barrett's break.
"I had a chuckle with him about the amount of time he took the line on. He's not a big lad ... but he said the option was there and he had to take it.
"He was brilliant."