Davies, who was a second-half substitute against PSG on Wednesday, has struggled with muscle injuries this season, and Bayern's medical team confirmed on Friday that the fullback's club season was practically over.
Davies has made just six Bundesliga starts this season, and he has not completed 90 minutes in a match since February.
With Bayern knocked out in the Champions League semi-finals, the German champions have only three matches left this season, including a Cup final against Stuttgart on May 23rd.
But the timing could hardly be worse for Canada, who are set to co-host the World Cup from June 11th. The 25-year-old serves as captain for his country, who begin their group campaign against Bosnia on June 12th.
Davies's injury woes have been mounting this season, with the defender already missing friendlies against Iceland and Tunisia in March due to a hamstring strain.