Bale scored the opener in a 3-1 Copa del Rey win over Unionistas de Salamanca but was unable to continue beyond the 53rd minute midweek.
Wales star Bale, who has battled injury and illness this season, was making his first appearance since the LaLiga victory against Getafe on January 4.
"He's twisted his ankle a bit," Zidane said. "I don't think it's much but, as always, we'll see tomorrow. He couldn't go on."
Bale's forced withdrawal appeared to unsettle Madrid, who conceded a stunning equaliser four minutes later as Alvaro Romero surged forward and fired past goalkeeper Alphonse Areola.
Juan Gongora's own goal after the hour and a late Brahim Diaz strike saved Zidane's men from an upset and extended their winning streak to five games in all competitions.
The Los Blancos boss insisted he was satisfied despite flirting with a premature exit against the third-tier minnows.
"It was a tough night at a tough place to come and play," he said.
"We struggled with moving the ball and we didn't see much great football, but that was down to the pitch, not more than that.
"We're pleased because in the end we're going through to the last-16 and that's what we came to achieve."
Madrid - level on points with leaders and defending champions Barcelona - visit Real Valladolid in LaLiga on Sunday.