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The Chile international sustained the problem in the Telekom Cup final on January 14, where Bayern defeated Mainz 2-1.
Vidal did start against Freiburg as the champions returned to Bundesliga action with a 2-1 success on Friday, but he could not complete 90 minutes and was forced off early in the second half.
Carlo Ancelotti’s side face the Gunners in the first leg of the tie at the Allianz Arena on February 15, and Vidal has his sights set on that meeting as a potential date for his return.
“I feel bad and have severe pain on the rib. Now I will have to pause, because I cannot play,” he told TZ.
“I already missed training for a week, but now it should take at least two or three weeks.
“[I will see] how I feel for the last 16 in the Champions League.”