The 33-year-old suffered a torn ligament in training on Friday and could be sidelined for most of the rest of the season following Saturday's surgery
The 33-year-old, understudy to Bayern's regular No.1 Manuel Neuer, has made just two Bundesliga appearances this season.
With the title already assured, Starke was named in Bayern's starting XI against his former club Hoffenheim last week, which ended in a 3-3 draw.
However, Starke is now set for a spell on the sidelines, though the German and European champions have not put a timescale on his return.
"Treble winners FC Bayern must give up on the services of Tom Starke for now," a statement on the club's website read. "The No.2 of the record German champions retired from training on Friday with a torn ligament to his right elbow.
"The 33-year-old goalkeeper underwent surgery on Saturday by a specialist in Tubingen. How long Starke has to stop is still open."
Starke made the switch to the Allianz Arena ahead of the 2012-13 season, but has been limited to just five Bundesliga appearances for Bayern.
Teenager Leopold Zingerle replaced him in the squad for Bayern's encounter with Augsburg later on Saturday.