"The operation went well," Mueller-Wohlfahrt said on the German soccer federation website (www.dfb.de).
"Now we hope that Sami will be back to fitness for the World Cup in Brazil (starting in June)," he added.
Real confirmed the success of the surgery, which took place under the supervision of club doctors at a clinic in Augsburg, Germany on Saturday.
"Over the next three weeks the player will follow a specific recovery plan so the injured ligaments heal correctly," the Spanish club said on their website (www.realmadrid.com).
Khedira is expected to be out for around six months after damaging the knee in Friday's 1-1 draw with Italy.
Germany coach Joachim Loew said it was a "bitter setback" but that he was optimistic he would recover in time to feature at the finals in Brazil.
Khedira's enforced absence is a blow for Real, who have only just got his midfield partner Xabi Alonso back after a five-month injury layoff.
Alonso suffered a bruised ankle in Spain's 2-1 win in a friendly against Equatorial Guinea on Saturday but coach Vicente del Bosque said it was nothing serious.
(Reporting by Iain Rogers, editing by Martyn Herman)
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