The 28-year-old, whose contract with the Yorkshire club expires in June, had surgery to repair damaged cartilage in his knee and will therefore miss the remaining two games of the season.
Injuries have regularly interrupted Somma's career at Elland Road, during which he has scored 13 goals in 39 appearances, including 12 in 2010/11.
He has played only six times since rupturing ligaments in a pre-season match in 2011.
Leeds manager Brian McDermott said: "He's not okay. He's done his cartilage and he's had an operation. It's very unfortunate for him.
"I don't know exactly how serious it is at the moment but he needed it done."
Leeds originally signed Somma on a short-term basis after bringing him to England on trial from American side San Jose Earthquakes.
He has previously played for Italian sides Perugia, Pro Vasto and Olbia and represented his country at full international level.