The Holland international was forced to pull out of the Oranje squad for the Euro 2012 qualifiers against Moldova and Sweden on Wednesday and, after flying back to Munich, went under the knife on Friday morning.
The procedure means the 27-year-old will be out for at least 10 days.
A Bayern statement read: "Over the past few days some inflammation has developed around the pubic bone.
"That tissue was successfully removed this morning.
"The medical department expects Robben to be able to resume training in 10 days' time."