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 this 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."Robben has barely played for Bundesliga leaders Bayern this season due to injury.
Chairman Karl-Heinz Rummenigge admits the former Real Madrid man is key to their ambitions domestically and in Europe.
He told the club's official website, www.fcb.de: "Take his brief comeback against Leverkusen: he was greeted by the crowd with a standing ovation. That doesn't happen to many players at Bayern, so our supporters understand what it means to have Arjen Robben at this football club.
"He's a superb player, a player who can win matches on his own. The task now is to get him back to full fitness. That's what we're working on, and I know we'll see a huge return from Arjen Robben in the fut