The winger has undergone surgery and will be absent for several weeks, meaning he will miss the last-16 clash with the Gunners
The France winger, 30, was absent from the Bavarians' 2-0 win over Nurnberg on Saturday with the injury and went under the knife on Thursday in a bid to completely eradicate the problem.
"An examination on Monday revealed that the nerve which had been under pressure from a bruise was completely removed in surgery last Thursday," the club announced on their official website.
"After healing, the 30-year-old is scheduled to begin [his recovery] later this week with exercise therapy and a week later should enter back into running training.
"This means Ribery will be missing from the next few games, including in the first knockout round first leg of the Champions League with Arsenal."
The Champions League holders travel to the Emirates on February 19 before the return leg on March 12.