The 32-year-old was forced from the field 68 minutes into his side's 4-2 Bundesliga victory over Hertha Berlin at the weekend, with subsequent tests revealing a tear.
Leverkusen issued a short statement on Wednesday to confirm that Rolfes will now undergo an operation on his right ankle.
"In consultation with the medical department of Bayer 04 it was decided after considering all options to follow an operative procedure," it read.
Rolfes conceded his disappointment, but vowed to return to action as soon as possible.
"This is obviously very frustrating for me but I will do everything to get back as quickly as possible," he said.
Leverkusen have kicked off the season with five consecutive wins in all competitions.
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