The 26-year-old right-back, who also played in the 2006 World Cup, has won 64 international caps and scored three goals, making him among the most experienced players in the squad.
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"Lahm has played in his position with great class and will take over the role of captain," Low told reporters at their Italian training camp.
Low also appointed 24-year-old Neuer as the team's first-choice keeper, with Werder Bremen's Tim Wiese as second choice and Bayern Munich's Hans-Jorg Butt third. Neuer will replace Rene Adler as Germany's starting keeper after he pulled out with a rib injury
"With our young team we want to have the responsibilities shared by several players," Low said.
"Bastian Schweinsteiger, on the pitch, will play the role of Ballack and interpret it in his way while Philipp Lahm will become captain. Schweinsteiger will be the vice captain," Low said.
Goalkeeping coach Andreas Kopke said choosing the 1.90m-tall Neuer, who has three caps, was not easy given the quality of his rivals.
"We had to act after Alder's injury. We decided to go with Neuer into this World Cup and he will be in goal against Hungary in the friendly tomorrow," Kopke said.
"It was a tough decision. Wiese had a very good season and Butt played in the Champions League final. Now it is important to help them put away their frustration."
Germany's 27-man preliminary squad has already been reduced to 25 following the injuries to Ballack and midfielder Christian Traesch.
Low said he was in no hurry to finalise his 23-man squad and would do it just before the June 1 deadline.
"I will take that decision only when I really have to because I want to keep my options open and have seen that players can always get injured," Low said.
Germany, whose final friendly match is against Bosnia on June 3, have been drawn with Australia, Ghana and Serbia in Group D of the June 11-July 11 tournament in South Africa.
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