The two players are isolating at home, in accordance with health protocols.
"Real Madrid announces that our players Marcelo and Luka Modric have tested positive for COVID-19," the club said in a brief statement.
Real Madrid's squad had returned to training on Wednesday after two days off, following their 2-0 win over Atletico Madrid in LaLiga on Sunday.
Modric, 36, started that game, playing the full 90 minutes, while Marcelo, 33, was an unused substitute.
On Tuesday, Real Madrid had announced positive test results for the coach of the club's basketball team, Pablo Laso, and point guard Thomas Heurtel.
Spanish football has seen an increase in COVID-19 cases in recent days, with positive results at LaLiga clubs Valencia -- including their manager Jose Bordalas -- and Levante, as well as LaLiga 2's Leganes and Eibar.
Real Madrid host Cadiz in LaLiga on Sunday, before travelling to Athletic Bilbao on Dec. 22 in their last game of 2021.