Trapp tripped and fell during a publicity shoot for the Germany Under-21 team on Monday.
Scans have revealed the 22-year-old suffered a break that is set to jeopardise Eintracht's European ambitions.
"The injury to Kevin Trapp is unfortunate for Eintracht Frankfurt and certainly a major setback," Eintracht chief executive Heribert Bruchhagen told the club's website.
"The medical prognosis is especially bitter. The probability that Trapp will play again is very low.
"We will discuss together with the German Football Association and analyse exactly how the accident happened."
Trapp offered his version of events to Bild, saying: "I don't know what happened. I started walking and all of a sudden I was down on the ground."
His agent, Dirk Hebel, added: "Somebody caught Kevin's heels and he slipped."
Trapp, who is to have surgery on Friday, has been a key part in Eintracht's unexpected fight for European football after only returning to the Bundesliga this season.
The club currently sit fourth although they have failed to win in their past six league games.
Trapp is likely to be replaced by 38-year-old Macedonian goalkeeper Oka Nikolov, who has made more than 350 appearances for the club.