The 40-year-old midfielder sustained the injury during Sunday's 0-0 Serie A draw against Juventus at the San Siro, leaving the pitch after a clash with Italian international Manuel Locatelli. The full extent of the damage only became clear afterwards, with AC Milan confirming on Monday that Modric had suffered a complex, multi-fragment fracture of the left cheekbone.
Surgery was performed at the La Madonnina Clinic in Milan by Dr. Luca Autelitano's team in the presence of Milan's medical staff, and the club confirmed the operation was a complete success.
Modric will have his stitches removed next week and will then begin a graduated return to training, initially limited to running and gym work with no physical contact permitted. His training load is set to increase progressively through to around 23 or 24 May, after which a decision will be made on whether he travels to Zadar with Croatia or continues his preparation in Milan.
The World Cup begins on 11 June in North America, leaving Modric approximately six weeks from surgery to be ready for tournament football. Recovery from this type of fracture typically requires six to eight weeks, and he may need to wear a protective mask to play.
Croatia head coach Zlatko Dalić moved quickly to express confidence in his captain's recovery.
"I am convinced that he will do everything to be ready for the World Cup, and we will provide full support," Dalić said. "I am confident that the recovery will go according to plan and that Luka, as team captain, will lead us at another major competition this summer."
Croatia face England, Ghana and Panama in Group L. This would be Modric's fifth World Cup.