The La Liga champions head into the second leg of their last-16 tie looking to overturn a 2-1 deficit; Zidane's side lost in the Spanish capital in February, prior to the tournament being halted due to the coronavirus pandemic.
The seldom-used James Rodriguez was also left out of the squad.
Bale didn't play a single minute in any of Real Madrid's final seven matches of the La Liga season, indicating Zidane doesn't view the Welshman as a key member of the team moving forward.
Zidane said as much last summer, openly stating his desire for the 31-year-old to leave the club prior to the season. The winger ultimately made just 16 league appearances during the campaign.
Captain Sergio Ramos, who is suspended for Friday's match after picking up a red card in the first-leg defeat, was included in the traveling squad for the contest at the Etihad.