The 27-year-old suffered the injury in the warm-up before Bayern's 1-1 draw at RB Leipzig on Saturday.
Jerome Boateng replaced him in the starting XI, with Lucas Hernandez moving to the left side of defence.
Bayern did not confirm a timeline for Alaba's return but it is believed he will miss several weeks of action, meaning head coach Niko Kovac will now have to weigh up his options for Wednesday's Champions League home clash against Red Star Belgrade.
"Bayern will be without David Alaba for a spell after the Austria international tore a muscle in his left thigh while warming up for Saturday's top Bundesliga match away to RB Leipzig," the club confirmed in a statement.
"The diagnosis was announced on Sunday following an examination by the FC Bayern medical unit headed by chief medical officer Dr. Hans-Wilhelm Müller-Wohlfahrt."
The German champions remain two points behind leaders Leipzig, while Borussia Dortmund sit second.
Bayern are one of three sides yet to lose in the Bundesliga this season, and have conceded just four goals in their two wins and two draws.
The injury will likely see Hernandez remain on the left side of defence for the next couple of weeks, with 18-year-old Alphonso Davies another possible option in that position for Kovac.
The reshuffle could also either see Boateng or Benjamin Pavard stand in at centre-back for the upcoming European visit of Red Star.
The Serbian champions travel to Allianz Arena on Wednesday sitting second in their league with two games in hand, after six wins from their opening six games.
They did, however, require two last-minute goals from striker Milan Pavkov in order to achieve their latest victory.
The 25-year-old arguably poses the greatest threat to a now-weakened Bayern defence, with the striker no stranger to big goals after netting a brace in Red Star's 2-0 victory over Liverpool last season.