The Germany defender, who had only returned this year after more than two years out with a double ligament tear, will leave for the United States in the coming days where the operation will take place.
"Obviously I am bitterly disappointed," Badstuber said in a statement.
"I am, however, optimistic and will return fully healthy. I know Bayern will do everything for me so that I return as an important part of the team."
Bayern, who have been plagued by injuries in recent months, were without several key players in their 6-1 victory over Porto, including Arjen Robben, Franck Ribery, Medhi Benatia and Bastian Schweinsteiger.
They could win the German league title this week and also play Borussia Dortmund in the last four of the German Cup as they look to repeat their 2013 treble-winning season.
(Reporting by Karolos Grohmann; editing by Toby Davis)
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