Defeat against Napoli was doubly painful for the Bundesliga giants, who face the loss of two important squad members for the start of the 2012-13 campaign
Alaba struck a first-half opener, before Paolo Cannavaro and Goran Pandev put the Italians in the driving seat. Xherdan Shaqiri equalised with 15 minutes to spare, but Lorenzo Insignie struck the winner to hand the Serie A side a convincing friendly victory.
It has now been announced that Alaba suffered a stress fracture in his left foot which would rule him out of contention for six to eight weeks, with the Austrian international out of the pre-season tour of the Far East.
The 20-year-old will be examined in detail on Monday, according to the club's official website, and a decision on treatment will be made then.
Rafinha meanwhile pulled ligaments in his ankle, but will not require surgery, with the right-back expected to be sidelined for four to five weeks.
Bayern open their Bundesliga campaign away to Greuther Furth on 24 August.