The club announced the news on Sunday (AEDT), having carried out the latest round of tests on Friday.
Hazard and Casemiro were the only two found to have contracted coronavirus, with the rest of the squad and staff given the all-clear.
"Real Madrid CF announces that our players Casemiro and Hazard have given positive results in the COVID-19 tests carried out Friday morning," a club statement read.
"All the other players and the coaching staff of the first team, as well as all the club employees who work directly with them, gave negative results in that same test carried out yesterday.
"Likewise, it is confirmed again that all, with the exception of Casemiro and Hazard, have given negative results in the antigen tests carried out this morning."
Zinedine Zidane's side faces Valencia on Monday (AEDT) after enjoying a 3-2 UEFA Champions League win over Inter Milan in midweek, with both Hazard and Casemiro in the starting XI for that European fixture.
Former Chelsea star Hazard ended a year-long goal drought against Huesca in Madrid's previous LaLiga outing, a 4-1 home win.