Modric suffered a thigh injury in the 4-2 defeat to Girona in La Liga on Tuesday.
The 37-year-old will miss Los Blancos' weekend game against Almeria and Real Sociedad in midweek.
Real Madrid play Osasuna in the Copa del Rey final next weekend before hosting Manchester City in the Champions League semi-finals.
"He got an injury in the game against Girona. We will see how he progresses in the next few days," Real Madrid manager Carlo Ancelotti said ahead of the game against Almeria.
"He will be doubtful for the Copa final. We must evaluate him, we are hurt, but it can happen. I hope he recovers for the important matches.
"We have very important midfielders like Federico Valverde, Eduardo Camavinga and Aurelien Tchouameni. We have many resources.
"But to replace Luka… you cannot replace his experience in these kinds of games."
Modric has made 46 appearances across all competitions for Real Madrid this season, scoring six goals and providing four assists.
