Injured Modric ruled out for three months
The midfielder suffered the injury 28 minutes into Croatia's Euro 2016 qualifier with Italy at the San Siro on Sunday, a game that ended 1-1 in Group H.
Real had been awaiting test results to reveal the issue's severity, and their worst fears have been confirmed by the Croatian Football Federation (HNS), with Modric's participation likely curtailed until next year.
"Croatian national team and Real Madrid midfielder Luka Modric will be away from the football pitch for about three months after the injury sustained in the counter with Italy," a statement read.
"Modric asked to be substituted after experiencing pain in the muscle, and MRI scans in Madrid have showed it is a serious injury.
"Modric will be away from the pitch for about three months. Surgery will be needed."
Madrid coach Carlo Ancelotti will now have to find a replacement for Modric alongside Toni Kroos in midfield, with Sami Khedira and Asier Illarramendi likely to battle for that starting place.