Somma, 28, returned to first-team action in December after more than a year out due to knee ligament damage, but required an operation to resolve a cartilage problem after making just six appearances.
The South African has played hardly any football over the last two seasons after initially suffering anterior cruciate ligament damage in July 2011, with various comebacks ending in bitter disappointment.
"He's done his cartilage and he's had an operation," manager Brian McDermott said after the weekend defeat at Birmingham.
"It's very unfortunate for him. I don't know exactly how serious it is at the moment, but he needed it done."
Somma arrived at Leeds from San Jose Earthquakes in October 2009 and after struggling to force his way into the first team went out on loan to Chesterfield and Lincoln.
He returned to Leeds at the start of the 2010/11 season and became a regular in then boss Simon Grayson's side, scoring 12 goals in 32 appearances before suffering his initial injury during pre-season training the following summer.