The 29-year-old picked up the knock while representing Croatia against Italy and it was confirmed that he would be sidelined until February after he underwent further tests.
Modric says he expected bad news from club doctors but says the extent of the blow came as a real shock to him.
"It's a despair," he told Sportske Novosti.
"The real shock came when the doctors told me that my recovery would last for three months. I was speechless.
"I thought I'd be out for some time, but I never imagined it could be for three months."
Modric also revealed that Madrid coach Carlo Ancelotti has urged him to return stronger than ever, but not to rush his comeback.
"He told me to listen to the doctors and not to rush the rehabilitation process. I'll do my best.
"I'll be in Madrid for a week receiving therapy then we'll see what we're going to do."