The club confirmed the Spaniard will miss both quarter-final games against Manchester United and the semi-finals should Bayern progress.
Bayern coach Pep Guardiola said: "It's bad news. We're going to miss him a lot."
Thiago suffered the injury in the first half of Bayern's 3-3 draw at home with Hoffenheim.
An MRI scan late on Saturday by team doctor Hans-Wilhelm Mueller-Wohlfahrt confirmed the extent of the injury.
Team-mate Thomas Muller said: "It's very bitter and comes at a catastrophic time, just before the important games."
Bayern clinched the Bundesliga in record time on Tuesday and hope to defend their Champions League crown.