The 26-year-old, whose last appearance was on Matchday 21 against Borussia Dortmund, underwent surgery to repair damaged ligaments on Tuesday and will not return to fitness before the end of the campaign.
The Brazilian was an ever-present in the Frankfurt backline in the first half of the season, starting 14 Bundesliga games and playing every minute of every group game in the UEFA Europa League. Since the turn of the year, however, he has managed just 32 minutes of league action, with Alexander Madlung replacing him in the first team. Anderson has made a total of 56 top-flight appearances for Eintracht and previous club Borussia Mönchengladbach.
Meanwhile, captain has also had to go under the knife to repair a broken nose suffered in last weekend's 1-1 draw at Hamburger SV, although the Swiss international is expected to be available for this weekend's relegation battle at home to SC Freiburg. Armin Veh's side currently sit in 13th place in the table.