The 33-year-old, understudy to Bayern's regular number one 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.
"Goalkeeper Starke has suffered an injury in training - elbow surgery today. Hopeful he'll return soon," read a post on Bayern's official Twitter account.
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 will replace him in the squad for Bayern's encounter with Augsburg later on Saturday.
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
