Hazard made a slow start to life with Real following his switch from Chelsea for a reported 100million euros over the summer.
The Belgian did not find the back of the net until October 5 when he registered in a 4-2 home victory over Granada.
He has failed to add to that tally but has raised the level of his performances to the delight of Zinedine Zidane and the Los Blancos faithful.
Hazard started Tuesday's Champions League Group A clash with Paris Saint-Germain, which ended 2-2, but he had to be withdrawn after 69 minutes.
The forward caught a blow on his right ankle from countryman Thomas Meunier and limped off the field with the help of the club's medical staff.
The talented schemer was taken straight to the hospital on crutches, where he still had time for a selfie with a fan, for further assessment.
It is understood that tests ruled out a break, but he will need to be checked over again in a couple of days after the swelling reduces.
Zidane said: "There is a little worry over Hazard at full-time. He was in pain at full-time, and we think it is more than an impact injury. It is a sprained ankle, but hopefully not a severe sprain. We will know more in the coming days."
The Frenchman is hoping for some positive news in the coming days but the prognosis does not look great as Real head into a crucial period of the season.
They play six times over the next three-and-a-half weeks across all competitions and Zidane would love to be able to call on Hazard.
The first El Clasico of the season is due to take place for December 18, having been rescheduled following unrest in the Catalan region earlier this month.
With the title race currently a closely-fought battle between table-topping Barcelona, Real in second and third-placed Sevilla, Hazard's absence would be a huge blow.