On Friday it was confirmed the Belgium forward has suffered a "muscular injury to the anterior part of his right thigh".
Hazard medical report.#RealMadrid— Real Madrid C.F. 🇬🇧🇺🇸 (@realmadriden) August 16, 2019
Los Blancos did not state how much action the big-money signing from Chelsea will miss, but his bow in LaLiga is set to be delayed.
"His recovery will continue to be assessed," Madrid said on their website.
Reports in Spain suggest Hazard will miss a few weeks of action and may not feature for Madrid until after the first international window in September.
It leaves head coach Zinedine Zidane facing a selection dilemma and may see an unlikely opportunity for Gareth Bale, who appeared destined to leave the Santiago Bernabeu in this transfer window.
James Rodriguez, who also looked set to depart the club, Lucas Vazquez and Vinicius Junior provide other options for Zidane in the absence of Hazard.