Klose, who suffered a freak injury when he stepped into a hole during Bayern's weekend win at Bochum, was initially expected to be sidelined for two weeks.
However, Bayern confirmed that the 30-year-old will be out of action for six weeks after undergoing surgery in Switzerland on Monday.
Klose's injury adds to the Bundesliga champions' woes, as they already have influential duo Franck Ribery and Luca Toni on the casualty list.
Bayern's leading goalscorer so far this term will miss several Bundesliga games, in addition the Champions League quarter-finals first-leg tie.
Moreover, he is set to miss his country's 2010 World Cup qualifiers with Liechtenstein and Wales.
"The injury to Miroslav Klose is obviously regrettable, but we hope he regains fitness as quickly as possible, and returns to the action for Bayern at least for the closing stages of the season," commented Germany coach Joachim Low.