Trapp suffered the injury during a publicity shoot with Germany's Under-21 team on Monday and tests in Frankfurt on Tuesday revealed fractures to his left hand and middle finger. He will have the operation on Friday.
"It is a regrettable injury and a major setback for Frankfurt," club boss Heribert Bruchhagen said. "The chance of him playing again this season is minimal."
"We will discuss these results with the DFB (German football association) and examine in detail the process of the accident."
It is still unclear exactly how the 22-year-old was injured.
Trapp has played in every game this season and his outstanding form has helped the promoted club rise to fourth place in the Bundesliga and into contention for a Champions League spot.