The Argentine striker fell awkwardly after getting his studs trapped in the turf just seven minutes into the first leg of the last-32 clash and was stretchered off in agony.
"Unfortunately, this injury rather ruined the night," Inter boss Andrea Stramaccioni told reporters. "It is a lesion to the anterior cruciate ligament, damage to the collateral ligament and capsule. It is a terrible injury and totally new compared to the problems he had in the past.
"There's a 1% chance of this happening, but it happened to Diego. We now just need to know when he'll have the operation.
"It's awful news, as we all care for him as a person as well as a player. I am personally very close to him and feel so sad right now."
Inter take a two-goal lead into the second leg with Rodrigo Palacio bagging a brace at the San Siro.