Alaba suffered an ankle knock in Austria's World Cup qualifying clash with Georgia and had to be withdrawn prior to half-time on Tuesday.
The length of the lay-off has not yet been determined, but it leaves head coach Carlo Ancelotti without either of his natural left-back options as Juan Bernat continues his recovery from ankle surgery.
However, there is some good news for the Italian with midfielder Sebastian Rudy cleared of injury.
The 27-year-old was taken off as a precaution in Germany's 6-0 rout of Norway but has been deemed fit to re-join training on Thursday.
German champions Bayern visit unbeaten Hoffenheim in the Bundesliga on Saturday.