Hazard only recently returned from a fractured right ankle so the sight of him appearing to have another problem in the same area was alarming for Zidane.
Madrid face Pep Guardiola's City in the first leg of their Champions League last-16 tie on Wednesday before a Clasico date with new LaLiga leaders Barcelona next weekend.
"It doesn't look good," Zidane told reporters at a news conference.
"It can become weak where you've had an injury. It is a blow, let's see.
"It's sore now but we'll see tomorrow when we do more tests."
It was a thoroughly miserable outing for Madrid as they suffered a surprise defeat thanks to Jose Luis Morales' stunning late effort.
Madrid drew 2-2 with Celta Vigo at home in their previous outing and they will host Barcelona next Sunday knowing they are now two points behind their great rivals in the title race.
Captain Sergio Ramos revealed the level of frustration he was feeling in a social media post.
"We're p***ed off," he wrote on Twitter.
"But we can't allow our heads to drop.
"We have to reset now and tomorrow push harder than ever before for a very important week. We're counting on you."