The 23-year-old picked up the problem in Sunday's 0-0 draw with Werder Bremen, and the news provides a huge blow to coach Armin Veh on the eve of the club's UEFA Europa League last 32 second leg against Porto, with the tie locked at 2-2.
Rode may now have played his last game for Frankfurt as he intends to leave when his contract expires after this season, with Bundesliga and European champions Bayern Munich reportedly set to sign him.
"Sebastian Rode got injured against Bremen," Veh said. "He will need an operation and will likely be out for the season.
"Rode's injury is very disappointing for him and for us, and for me on the eve of such a big game."
After securing a draw with Porto in the first leg at Estadio do Dragao, Frankfurt have two away goals to take back to Germany.
But Veh insists the Portuguese champions remain more likely to progress.
"Porto are still the favourites but we're playing well," he added. "But they were favourites in the first leg. We had a chance in that game and we have the same chance now."
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