The Belgium forward hobbled off in the second half of the 1-0 loss to Levante on Sunday (AEDT) and could be seen on the bench receiving treatment on his lower right leg.
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 faces Pep Guardiola's City in the first leg of a UEFA Champions League Round of 16 tie on Thursday (AEDT) before a Clasico date with new LaLiga leader Barcelona next Monday (AEDT).
"It doesn't look good," Zidane said.
"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.
💥 This BULLET from @jose1987morales stunner @realmadrid late to earn victory for @LevanteUD and break open the upcoming #ElClasico against @FCBarcelona for Los Blancos. More here ▶️ https://t.co/XeKQ28RcvE | #LaLiga | #LevanteRealMadrid pic.twitter.com/Pnk45zmzcg— beIN SPORTS (@beINSPORTS_AUS) February 23, 2020
Madrid drew 2-2 with Celta Vigo at home in its previous outing and will host Barcelona next Monday (AEDT) knowing it is now two points behind its great rival 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.
We're pissed off, 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.#HalaMadrid https://t.co/I50gYI3qef— Sergio Ramos (@SergioRamos) February 22, 2020
"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."