The 33-year-old limped out of Saturday's 2-2 draw with Hanover after just 30 minutes following a heavy tackle and underwent an MRI scan on Sunday morning which revealed the damage.
It is the latest injury blow for the 98-times capped Ballack, who returned to the club where he established his reputation after not having his contract renewed at English Premier League champions Chelsea at the end of last season.
Having missed the World Cup after damaging ligaments in his right ankle, Ballack was left out of the Germany squad for this month's Euro 2012 qualifiers against Belgium and Azerbaijan.
The match against Hanover was only his third game back as he tries to regain fitness after the ankle injury, but will now miss the qualifiers against Turkey in Berlin on October 8 and Kazakhstan in Astana four days later.
However, he insisted in an interview before the result of the scan was known that he would carry on as he always had done in previous trying circumstances.
"I will do what I have always done," he said and added there was no need to "make any drama" out of his new injury.
National coach Joachim Loew has said he will select Ballack for the Germany team only when he is fit enough and has proved his form and he faces a race against time to be fit for the friendly against Sweden on November 17.
While Loew has said that a fully-fit Ballack would also regain the captaincy from Philipp Lahm, who stood in so successfully for him in South Africa, his standing within the squad has dropped in the wake of Germany's third place finish in the World Cup finals.
"The last few weeks of course were not easy for me. They have shown me how things are," said Ballack.