Tests undertaken on Friday (AEST) confirmed an adductor issue for midfielder Modric, who looks highly likely to miss this weekend's LaLiga fixture against Levante.
Zinedine Zidane's men then commence their UEFA Champions League campaign away to Paris Saint-Germain on Thursday, before returning to Spain for a tough trip to Sevilla.
Modric, 34, completed two full matches for Croatia during the international break but now joins Isco, Marco Asensio and Brahim Diaz in the treatment room, while James Rodriguez and Eden Hazard have also suffered in recent weeks.
Madrid's statement read: "Following the tests carried out on our player Luka Modric by Real Madrid's medical department, he has been diagnosed with a muscular injury to the adductor in his right leg.
"His recovery will continue to be assessed."
Modric's appearances in Euro 2020 qualifying for Croatia included a goal against Azerbaijan, the Ballon d'Or winner converting a penalty in the 1-1 draw.