A bruise that has pressed on a nerve saw Ribery undergo surgery on burst blood vessels last Thursday. He is scheduled to begin his rehabilitation this week before resuming running next week, according to Bayern's official website.
But the trip to face Arsene Wenger's side on Wednesday February 19 comes too soon for the Ballon d'Or nominee.
It is unclear whether or not Ribery will be fit in time for the return leg at the Allianz Arena on Tuesday March 11, but the three-week gap should give the France international every chance to recover.
Arsenal faced Bayern at the same stage of last year's tournament. They won the second leg 2-0 in Germany, but a 3-1 loss in the first leg saw them eliminated on away goals.
Bayern progressed to win the tournament with a 2-1 victory over Borussia Dortmund in the final.
They are 13 points clear at the top of the Bundesliga after 20 games.