The 23-year-old Frenchman hurt his right knee which needed surgery in 2013 and has since suffered from inflammation.
With Madrid's latest Clasico clash with Barcelona looming on December 3 and Bale already ruled out, coach Zinedine Zidane said he could take no chances.
"He took a blow on his bad knee, the one that causes problems, so as usual we don't want to take risks. He has to rest and I hope it will be a lot better in two or three days," the coach told a press conference.
Varene, who scored in Real's Champions League victory over Sporting Lisbon on Tuesday, could be replaced by Sergio Ramos even though the Spaniard is one yellow card from a suspension.
Bale, meanwhile, is to undergo an operation on the right ankle he injured in Portugal.
"Gareth will be out a long time but we will try to continue on our path," Zidane said. The coach did not say how he would plug the gap caused by the absence of the club's record signing.
"We can change the system, but the dynamic of what we are doing on the pitch will not change. There are a lot of players who can play in different positions and that's the good side of this team," Zidane declared.