Bale took a painful blow to the right ankle during Madrid's 3-0 defeat by CSKA Moscow in midweek and was visibly struggling at the end of the game.
He didn't train on Friday when coach Santiago Solari intimated that Bale would miss the match against their Madrid neighbours.
"We will see how ankle improves from yesterday to today and from today to tomorrow," said Solari. "We will speak to the medical team and with him (Bale)."
Solari's decision to rest Bale means the Welshman has more time to recover ahead of the Wednesday's semi-final in the Club World Cup in Abu Dhabi.