Ballack out of World Cup finals
It was also a personal setback for 33-year-old Ballack, who was set to play at his third World Cup and is unlikely to get another chance to perform on the sport's biggest stage.
The Chelsea midfielder was injured in the first half of Saturday's FA Cup final against Portsmouth, limping off during during his team's 1-0 win after a late tackle by Kevin-Prince Boateng.
The ankle was so badly swollen that a planned scan on Sunday had to be postponed until Monday morning.
"There's naturally a lot of disappointment. It's bitter to get a diagnosis like that two or three weeks before the World Cup. But that's football. That happens. Life goes on," Ballack told German television.
"He (Germany coach Joachim Low) is naturally disappointed. I'll fly down there now and we'll let it all sink in," added Ballack, who broke off the interview and hobbled away on crutches.
Low said he had been shocked by the news.
"Michael Ballack is a very important player for us, in the decisive matches he often played a very, very important role for us, a central role for us," he said.
"I talked to Michael. He's deeply disappointed. He put all his energy and power into playing in this World Cup.
"He's near his 100th cap. That would have been a match in Frankfurt against Bosnia.
"That's an immense disappointment for him to not be able to play in this World Cup.
"I called the team together and passed along the information. It's very very unfortunate for us. But it shows we have to pull all our strength together and look forward. We've got a lot of young players."
The DFB said Ballack has suffered a tear of one ankle ligament and a partial tear of another.
"According to the diagnosis today by national team physician, Dr. Hans-Wilhelm Muller-Wohlfahrt, a complete recovery can be expected but a return to training will not be possible for at least eight weeks," said a statement.
German-born Boateng, booked for the tackle, is in the provisional squad of Germany's first-round opponents Ghana.
DFB president Theo Zwanziger expressed anger at the tackle.
"I'm deeply sad that Michael Ballack will miss the World Cup because of a foul like that. He has done an enormous amount for German football in the last few years and would have deserved to take part in this tournament," he said.
Ballack won the first of his 98 caps against Scotland in 1999 and helped Germany reached the 2002 World Cup final and third place four years ago, when they hosted the tournament.
Germany face Australia, Serbia and Ghana in Group D at the World Cup starting next month.
"It's bitter that the captain, with such experience is out of the tournament," Germany defender Philipp Lahm told reporters at Bayern Munich's training ground.
"I also feel personally sorry for him, because it would have been his last World Cup."
"It's a loss for the team, because of his personality and responsibilities, but I am convinced that we can still play a good World Cup without him," added Bastian Schweinsteiger, Lahm's Bayern and Germany team-mate. "We have a lot of quality."
Low was already under fire for leaving Schalke 04 striker Kevin Kuranyi out of the squad, despite the player's impressive tally of 18 Bundesliga goals this season.
Low's chosen strikers, Miroslav Klose, Lukas Podolski and Mario Gomez, have all struggled to hit the target.