Chivu was stretchered off following an accidental clash of heads with Sergio Pellissier.
The Inter staff announced the surgery had been "a success" and it is not clear how long he will have to spend on the sidelines in order to recover.
"The player sustained a trauma to the right side of the cranium and it provoked some fractures with the collapse of the structure and some blood, but the bruising was contained," explained Professor Franco Combi on the official Inter website.
"The surgery was necessary above all for this bruising and consisted of removing the bone fragments that had fallen towards the brain, emptying out the congealed blood and ensuring it did not form again in future.
"The cranium was reconstructed with the bone of the patient and is back to normal. It all went according to plan, so we are fairly confident he can recover without problems.
"It is premature to say when he can leave the hospital, but everything is in place for a good recovery."