Adler picked up the tendon injury during a friendly against Austria's Red Bull Salzburg on July 3 and last season's Bundesliga runners-up did not say how long they expected the player to be sidelined for.
"In order to have a problem-free season, surgery is unfortunately inevitable," the 26-year-old German number two said on the club website.
"That is a hard blow for us," Leverkusen Sports Director Rudi Voller added. "We will have to wait for the operation and then hope he comes back quickly."
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