The Spain international goalkeeper was hurt during Bayern's friendly with a Paulaner dream team of amateur footballers in Unterhaching on Monday, a match Pep Guardiola's men won 5-1.
Reina, who moved to the Allianz Arena in the close-season to provide back-up to regular number one Manuel Neuer, will now endure a period on the sidelines.
"Pepe Reina has suffered a serious calf muscle injury," read a statement on Bayern's official Twitter account.
"Our goalkeeper will be out of action for a number of weeks. Get well soon, Pepe."
The 32-year-old has yet to make his competitive debut for Bayern since joining from Liverpool.
Bayern's experienced third-choice goalkeeper Tom Starke is now likely to act as understudy to Neuer.
The Bavarians return to Bundesliga action against Werder Bremen on October 18 at the Allianz Arena after the international break.
‘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
