"Our players Casemiro and Hazard have given positive results in the COVID-19 tests carried out on Friday morning," Real said in a statement.
The club said that all other first-team players and coaching staff, as well as the club employees who work directly with them, had returned negative tests.
Real defender Eder Militao had tested positive for COVID-19 earlier this week and was forced to miss Tuesday's 3-2 victory against Inter Milan in the Champions League.
Real, who are a point and place behind La Liga leaders Real Sociedad with a game in hand, face 13th-placed Valencia on Sunday.
