Totti suffered the injury while scoring his second goal against Napoli and his knee has reacted badly to light training.
Totti is unlikely to be fit for the Europa League game with Fulham.
“The knee is swollen and that could be anything in this type of situation,” chief medic Professor Mariani told the Corriere dello Sport.
“I won’t rule out an operation on the meniscus ligament at this stage.”
