Casemiro limped out of Wednesday's 1-1 draw with Villarreal and resulting tests showed that the Brazilian has suffered a fracture to his left fibula, which will rule him out until after the next international break.
Marcelo will also miss this weekend's clash against Las Palmas with a calf problem, and Zidane has conceded that he is "always worried" when key players in his team pick up injuries.
"I've always worried when players get injured. Especially when they are players who are in the starting line-up, like Marcelo and Casemiro," Zidane told reporters.
"At the end of the day, we can't do anything about it. I hope the injuries are not as important as they seem and they are back quicker than we think. We have got a big squad to make changes and that is what we are going to do.
"It's clear that perhaps in the position of Casemiro there is no-one exactly like him, but we will just make some changes and be a little bit different."
Real Madrid currently sit top of La Liga on 13 points after winning four and drawing one of their five league matches this season.