The 22-year-old was injured tackling Germany team-mate Miroslav Klose in the first-half and is expected to miss the whole of April, but he should not need an operation. Bayern's defeat in Munich saw them lose top place in the Bundesliga to Schalke 04 who beat Bayer Leverkusen 2-0 also on Saturday with two goals from ex-Germany striker Kevin Kuranyi.
Stuttgart's medical staff say Khedira should be back for their last two Bundesliga matches before the season ends on May 9, with Germany coach Joachim Loew set to announce his World Cup squad the week before.
Khedira has won two caps for Germany and came on as a second-half substitute in this month's 1-0 defeat by Argentina in a friendly.
He is the second German player to announce he is in danger of missing the FIFA World Cup, which runs from June 11 to July 11. Hamburg's Marcell Jansen revealed he has an ankle injury which could also keep him out of the tournament.
Germany, who finished third as hosts of the 2006 World Cup, have drawn Africa Cup of Nations finalists Ghana, Australia and Serbia in Group D. They begin their campaign against Australia on 13 June in Durban.