Modric suffered the injury in a clash of heads with Juventus midfielder Manuel Locatelli in Sunday's 0-0 draw at the San Siro. He left the field with 10 minutes left.
Although clearly in pain, Modric remained on the bench until the end of the game without receiving medical treatment, but following an examination he will require an operation later on Monday.
Milan are third in the standings, 12 points behind leaders Inter Milan with four games remaining, and Modric is doubtful to take any part in their season run-in. A protective mask may be needed should he recover in time for the World Cup.
The World Cup, co-hosted by the U.S., Canada and Mexico, starts on June 11, and Croatia will face England, Ghana and Panama in Group L.