The Wales star returned to team training over the weekend but head coach Zinedine Zidane has decided the first leg of the round-of-16 tie has come too soon for him to play a part.
Toni Kroos has been passed fit for the 19-man squad but full-back Danilo and attacking midfielder Marco Asensio have been left out, as has 18-year-old Mariano Diaz.
Speaking at a news conference on Tuesday, Zidane suggested Madrid's LaLiga meeting with Espanyol may be the more realistic moment for Bale to make his first appearance since November.
"It's the first week that he's trained with the group," he said. "He's good, he's good physically and mentally, which is the most important thing.
"We'll see if he can be in the squad or if he'll be there at the weekend. At the same time, after two or three months out, we have to be very careful with Gareth."