The former Chelsea playmaker only made his long-awaited return from an ankle injury that forced him to miss 16 matches in the LaLiga tie at Celta Vigo last weekend, but began to limp during the second half of Saturday night's 1-0 defeat to Levante.
Hazard - who started for the second successive week - was finally substituted after 67 minutes in some discomfort at the Estadi Ciutat de Valencia, with manager Zinedine Zidane subsequently admitting that the situation "doesn't look good".
"Bad sensations," he said after the game. "It’s a knock on the area where he had his [ankle] injury."
Real's fears over a big setback have now been realised, with the club releasing a medical update on Sunday confirming that Hazard has sustained a fracture to his right ankle.
"Following the tests carried out today on our player, Eden Hazard, by the Real Madrid medical department, he has been diagnosed with a fracture to his right distal fibula," the report read.
"His recovery will continue to be assessed."
Hazard now looks set to miss both Champions League last-16 ties against City, who travel to the Santiago Bernabeu on Wednesday before the return leg in Manchester on March 17.
He will also be absent for next week's crucial Clasico against title rivals Barcelona in Madrid, with early reports in Spain claiming that the Belgian international is facing another two months on the sidelines.
While Real have yet to confirm a time-frame for Hazard's return, such a lay-off would rule him out for all but the final four weeks of the 2019-20 campaign.