Rolfes pulls out of performance test
Bundesliga leaders Leverkusen said the operation was to repair cartilage damage for Rolfes, who has only just returned following a three-month injury absence.
"This is a major shock for us," sporting director Rudi Voeller told reporters. "It is especially painful for Simon and we must now give him confidence and support him as much as we can. He must think positively."
Leverkusen said he would be out for several weeks. Rolfes also had two previous operations on the same knee last year.
The 28-year-old, who has won 21 caps since 2007, is looking to take part in his first World Cup in South Africa in June.
Rolfes felt pain in his knee during a brief appearance in Leverkusen's 3-0 win at Hoffenheim on Sunday.
Germany manager Oliver Bierhoff said he was not out of contention for a spot in the World Cup squad.
"One should not hurry to rule him out," Bierhoff told reporters. "We should keep our fingers crossed he comes back and plays soon."
Germany coach Joachim Loew said they would wait and see how long a recovery he would need but ruled out a return to the squad for Torsten Frings.
Loew informed the experienced Werder Bremen midfielder last week he would not feature in his World Cup squad.
"That is out of the question. This was a fundamental decision," Loew told the SID news agency.
"(Rolfes' injury) is a setback for us but we must first wait and see how long he will be out."