Hazard and teammate Casemiro have both tested positive and will be sidelined while they quarantine, a statement from the Spanish club said.
"Real Madrid C.F. informs that our players, Casemiro and Eden Hazard, have tested positive in the COVID-19 tests undertaken yesterday, Friday, in the morning.
"All of the other first-team players and coaching staff, as well as the club employees who work directly with the squad tested negative in yesterday's tests.
"Meanwhile, all of them, apart from Casemiro and Hazard, once again tested negative in the antigen tests taken this morning."
The news rules former Chelsea playmaker Hazard out of Real's next game against Valencia and Belgium's Nations League match against England on 15 November.
Meanwhile, Brazil's Casemiro would be unlikely to be allowed to feature in World Cup qualifiers against Venezuela and Uruguay.
For Hazard this is the latest in a series of setbacks following his 2019 transfer from Chelsea to Real Madrid for a fee reported to be worth £150m.
He has struggled for form, fitness and has faced frequent questions about his weight, despite still being crowned a LaLiga champion in his first season in Spain.
Injury has largely prevented him from showing why the club were so keen to sign him, while he angered his bosses by turning up to training after his summer move overweight.
And despite the title win last season, labelled it the worst of his career.
He seemed to be back to his brilliant best with a stunning goal - just his second for the club - against Huesca at the end of October and this latest setback will be a real source of frustration.
Eden Hazard's Real Madrid has gone from bad to worse with news of his positive coronavirus result.