Hazard suffered the injury following a challenge from international teammate Thomas Meunier in Real Madrid’s 2-2 draw with Paris Saint Germain in the UEFA Champions League last week.
It was initially believed that the Belgium national team captain would be out for up to ten days, making him a possibility for the crunch tie.
"After the tests performed on our player Eden Hazard by the Real Madrid Medical Services, in the process of the evolution of his right leg injury, he has been diagnosed with an external incomplete micro-fissure in that area," the club said in a statement on Thursday.
"His recovery will continue to be assessed."
Hazard joined Real Madrid in a big-money move from Chelsea in the summer but is yet to set the Santiago Bernabeu alight with the exceptional performances he is usually associated with.
The 28-year-old has scored just one goal and provided one assist from 13 appearances across all competitions for Los Blancos this season.
Ahead of the El Classico, Real Madrid are in La Liga action against Espanyol and Valencia while they complete the UEFA Champions League group stage with an away trip to Belgium to face Club Brugge.
Real Madrid and Barcelona are both locked on 31 points from 14 games with the Spanish champions only topping the table on goal difference.
