The Netherlands international scored the opening goal in Bayern's 2-0 DFB Pokal win over Augsburg on Wednesday evening but was forced to leave the pitch after only 16 minutes of play following a reckless challenge from Marwin Hitz.
The Bundesliga champion was initially hopeful that the attacker had merely sustained a little knock, but Robben's father - and agent - has now made it clear that the 29-year-old will not feature again in 2013 as he has also suffered ligament damage.
"He will not play again before the winter break," Hans Robben told NOS.
Robben - who has scored 13 goals in 20 appearances for Bayern this term - was understandably frustrated with his injury, but was adamant that he will be back to his usual best after the winter break.
"Of course, I am very disappointed. I was in great form and was looking forward to each game and now this happens. I will be back though, and we want to achieve the goals we have set for ourselves," the winger said.
Bayern has confirmed on its official website that the attacker will be out of action for six weeks.