The forward limped off after he suffered the injury in the 67th minute of Madrid's 1-0 defeat to Levante in La Liga on Saturday -- a result that left them two points behind Barca ahead of their meeting on March 1.
"Following the tests carried out today on our player, Eden Hazard, he has been diagnosed with a fracture to his right distal fibula," a club statement said. "His recovery will continue to be assessed."
Club sources have told ESPN that the Belgium international -- signed for €100 million from Chelsea last summer -- is expected to be out for about two months.
Hazard, 29, had just returned from an injury layoff of nearly three months after suffering a microfracture in his right ankle in November.
He has made just nine starts in La Liga this season, scoring one goal.
Madrid will also be without forward Rodrygo, who is suspended for the match following a second yellow and subsequent red card he picked up for celebrating a goal while playing for the club's B team.