Modric, Ballon d'Or winner in 2018, scored Real's opener in the victory, controlling a looping clearance from a corner with his chest before unleashing a sublime long-range volley which arrowed into the top corner in the 41st minute.
Luka Modric scored a brilliant goal from long range to help Real Madrid secure a 2-0 win against Girona on Sunday which took them back level with Barcelona at the top of La Liga.
"Our player Luka Modric is out of the game against Mallorca today because of a viral illness," said the Spanish champions in a statement.
Manager Carlo Ancelotti heaped praise on Real Madrid midfielder Luka Modric after the 39-year-old Croatian worked his magic with a terrific assist to help Vinicius Jr score the winner in a hard-fought 2-1 LaLiga win at Celta Vigo on Saturday.
The Super Cup triumph was Modric's 27th title with Los Blancos and it takes him past Nacho and Carvajal who have all won 26 titles.
The 38-year-old Ballon d'Or winner won a sixth Champions League crown as well as a fourth LaLiga title with Real last season.
Croatia captain Luka Modric said he would look to continue playing on despite his country's likely elimination from the European Championship after conceding a last-gasp goal in a 1-1 draw with Italy in their final Group B game on Monday.
The 38-year-old became the oldest goalscorer in European Championship history when he prodded home in the 55th minute to put Croatia on track to reach the knockout phase for a fifth straight major tournament.
Portugal, who won six of their previous seven matches against Croatia, begin their Euro 2024 Group F campaign against Czech Republic on June 18. Croatia face Spain in their first Group B fixture next Saturday.
Croatia coach Zlatko Dalic announced Monday a preliminary 26-man squad for Euro 2024 to be led by veteran captain Luka Modric in his likely last major tournament before retirement from international football.
It takes Real to 65 points ahead of Barcelona, in second after they beat Getafe 4-0 on Saturday, and nine in front of third-placed Girona before they host Rayo Vallecano on Monday.
Carlo Ancelotti's side are a point ahead of Catalan minnows Girona, who host Alaves on Monday and will be looking to reclaim pole position.
Both players appeared in 2017 as witnesses during the multi-million-euro corruption trial of former Dinamo Zagreb boss Zdravko Mamic providing details of their transfers from the current Croatia champions
Ilkay Gundogan has signed for Barcelona on a free transfer at the end of his Manchester City contract while Luka Modric will stay at Real Madrid for another season after renewing his deal until June 2024.
Croatia coach Zlatko Dalic on Monday appealed to star midfielder Luka Modric to stay amid growing speculation the captain will retire from international football.
Bruno Petkovic and Luka Modric struck in extra time to fire Croatia into the Nations League final with a 4-2 victory over hosts the Netherlands on Wednesday.
Even rivals paid tribute, with Real Madrid midfielder Luka Modric saying: "one of the best players I have played against."
Carlo Ancelotti believes Karim Benzema, Luka Modric and Toni Kroos will stay at Real Madrid next season, the Los Blancos coach told a news conference Friday.
Croatia beat Morocco 2-1 in the World Cup third-place playoff on Saturday to leave Qatar on a high after the European side failed to reach a second consecutive final.
