Having already missed training this month, Vidal, 29, aggravated a rib injury in Bayern's first game back after the Bundesliga's international break against Freiburg on Friday and was forced off after 55 minutes, replaced by Joshua Kimmich.
Speaking to tz, the Chile international said: "I feel bad. I have got severe pain in the ribs. I can't play like this and must take a break now," ESPN report. "Anyway, I've already missed a week's training. Now it looks like I'll need at least a further two or three weeks' break.
"Only be doing this can I completely recover. Then we will see how I feel for the Champions League game."
Vidal missed training on Monday due to the knock but they club are yet to decide whether the former Juventus' midfielder will be given the break he feels he needs.
A statement on Bayern's official website read: "FC Bayern were back in training on Monday afternoon after two days off. However, coach Carlo Ancelotti was without Aruto Vidal, who completed an individual session in the performance centre due to a bruised rib.
It continued: "Vidal will be on a reduced schedule for the next few days and will also be treated by the FCB medical staff. A decision about his return to team training will be taken on a day-to-day basis."
Bayern welcomes Arsenal to the Allianz Arena for the first leg of their last 16 tie on 15 February.
The Gunners have failed to make it beyond the first knock-out stage of the competition in the last six campaigns. During that period, they were twice eliminated by Bayern during the 2012-13 and 2013-14 campaigns.