The Italian confirmed that the Wales international will miss Sunday's trip to San Mames but expects the former Tottenham man to return for Wednesday's Madrid derby
The former Tottenham Hotspur man missed los Blancos' Copa del Rey quarter-final victory over Espanyol on Tuesday after picking up an impact injury against Granada last weekend.
Madrid face city rivals Atleti in the first-leg of their semi-final next week and Ancelotti is confident his cautious approach will pay dividends.
"[Gareth Bale] is fine, but I don't want to take risks,” he told a press conference.
"He's not available tomorrow because he didn't train this week. He's doing a good job and I think he'll be available for Wednesday.
"He doesn't need another pre-season, because the problem he has is very small.
"[Jese] is an option to replace Bale. We can also put [Asier] Illarramendi or [Angel] Di Maria on the right. We will look tomorrow.
While Bale is set to miss out, Real Madrid will be boosted by the return of Raphael Varane, who has been sidelined since November with a knee injury.
"Varane is on the list," Ancelotti added. "We need to be careful with him. The knee has responded very well, but he can't play every three days just yet."
Ancelotti also confirmed that he isn’t planning offloading either Casemiro or Fabio Coentrao, both of whom have been linked with moves away from the Bernabeu in recent months, while giving his backing to plans to renovate the stadium.
"Neither Casemiro nor Coentrao will leave the club," he said.
"I have seen the [new Bernabeu] project, it will be a fantastic stadium. I would enjoy it there, that's for sure."
The former Juventus, Milan and Chelsea boss also paid tribute to Spain's former Euro 2008-winning coach Luis Aragones, who passed away on Saturday.
"I'm very sorry for this loss, because he is a person who has been very important to football in Spain and around the world,” he said.
“Spain started to win in 2008 with Luis Aragones. He's been a figurehead for football.
"He gambled on a new way of playing, like [Arrigo] Sacchi or Ajax in the '70s."
Real Madrid sit third in La Liga, one point behind joint-leaders Barcelona and Wednesday's rivals, Atletico Madrid.