The 32-year-old has netted 19 league goals for Thomas Schaaf's side this season to top the Bundesliga scoring charts and help Frankfurt to eighth place with six games to go.
Meier did not feature in Saturday's 3-0 defeat at Bayern Munich and the club confirmed on Monday that he will miss the remaining weeks of the campaign as he needs an operation.
"The injury to Alex has hit us hard," Schaaf told the club's official website. "We had hoped that he could help us with goals in the final games of the season.
"We wish him well with the surgery and hope he returns healthy as soon as possible."
Frankfurt are four points adrift of the top six and welcome Borussia Monchengladbach on Friday.
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