Demichelis sidelined for at least six weeks
Demichelis was injured during training on Wednesday but his injury turned out to be more serious than initially expected. The club said he would be out between six and eight weeks.
"The duration of his injury break is bitter," said Bayern sports director Christian Nerlinger on the club website.
"We hope that his recovery period will be as quick as possible and he can be with us very soon."
Argentina, fourth in the South American qualifying group for the 2010 World Cup, meet leaders Brazil at home on September 5 and visit third-placed Paraguay four days later.
Argentina coach Diego Maradona said on Wednesday he feared injuries in next week's friendly against Russia in Moscow could weaken his side to face Brazil, never imagining a training mishap might deprive him of a first choice player.
Midfielder Juan Sebastian Veron and striker Carlos Tevez are nursing injuries and pulled out of Maradona's friendly squad on Wednesday.
The top four teams in the South American group qualify for the finals in South Africa. Argentina are only two points ahead of Ecuador in fifth place which is synonymous with a playoff against the fourth team in the CONCACAF region.