The Netherlands winger scored four minutes into the DFB-Pokal third-round clash, but was forced off 12 minutes later following a challenge by opposing goalkeeper Marwin Hitz and will now miss the club's FIFA Club World Cup campaign.
Robben's injury will come as a bitter blow to Pep Guardiola as he bids to add more silverware to his Bayern trophy cabinet following the side's UEFA Super Cup victory over Chelsea in August, with the reigning Champions League winners set to open their Club World Cup campaign on December 17 in Morocco.
A tweet on the club's official Twitter account confirmed Robben's setback, as it read: "Bad news: Arjen #Robben is seriously injured. The wound on his right knee is down to the bone. He will be out for 6 weeks."
And Robben expressed his disappointment at being sidelined.
"Of course I'm really disappointed. I've been feeling great and have been enjoying playing every game with the team," he tweeted through the club's account.
"But I will return to fitness and will join the team in tackling the goals we set ourselves for the season."
Robben has scored six goals in 12 Bundesliga appearances for Bayern this season.
