The Belgium international hobbled off in the second half of Madrid's 1-0 loss to Levante and scans the next day confirmed he suffered a hairline fracture to his right ankle.
Madrid did not put a timeframe on his return, but it marked a huge blow ahead of this week's Champions League encounter with Manchester City and the Clasico clash with Barcelona.
Zidane does not know if the 29 year-old - who had only just returned from a three-month absence with a similar issue - will be fit before the end of the campaign.
"I can't tell you. It is hard to say," he said at a news conference ahead of Wednesday's last-16 first leg with City. "We don't know if he will be operated on, but he's obviously not happy. He had been out for almost three months and then played two games and picked up an injury.
"Obviously it is very bad news for him, but I can't tell you if he's going to be back before the season is over."
Madrid is reportedly deliberating over whether to operate on Hazard, who is set to miss more action for Los Blancos in his maiden campaign than he did in seven seasons with former side Chelsea.
However, Zidane insists it is not a straightforward call to make and is simply hoping to see a fully fit Hazard back in action sooner rather than later.
"I'm not the right person to tell you what should have been done and what shouldn't have," he said. "Obviously we are not happy about his injury.
"It comes at bad moment and I feel bad for him because he wanted to play and help us and now he's out again. It is sad of course.
"I just hope when he's back again he's absolutely fit. That's what he wants and what we want. But it's a tough moment for him.
"I can't tell you what I see in his eyes but I can tell you he's not happy. It's very important for him to stay positive but it is a bad moment for him.
"It won't be easy and he will feel like that for some time. He loves being with us and helping us - that won't change - but knowing he can't play right now is very bad news for him."