Concerns over the 29-year-old arose when he was forced off the field during Bayern's 2-0 win over Augsburg in the DFB-Pokal.
The former Chelsea player was caught on the knee by the studs of opposition goalkeeper Marwin Hitz and limped off the pitch.
Following tests this morning, Robben told the club's official website: "Of course I'm bitterly disappointed. I was in such good form and was looking forward to every game I was playing, and now this happens.
"But I'll come back fit and will then help the team reach the goals that we set ourselves before the start of the season."
Robben will be unavailable for Bayern's Champions League clash against Manchester City next Tuesday.