Chelsea midfielder Ballack was ruled out of the tournament after injuring his ankle in the FA Cup final two weeks ago. Bayern Munich's Lahm, 26, will skipper the side with 64 caps to his name having made his international debut in 2004.
Low also confirmed midfielder Bastian Schweinsteiger as vice-captain, but along with Lahm, goalkeeper Hans-Joerg Butt and midfielder Thomas Mueller he will not feature in the friendly against Hungary in Budapest on Saturday.
The four Bayern Munich players will be rested and remain at Germany's training camp in north Italy having played in last Saturday's Champions League final defeat to Inter Milan. Against Hungary, Germany will be led by striker Miroslav Klose in their penultimate World Cup warm-up match before their opening game in Group D against Australia on 13 June.