Last weekend he was struggling in the first half against Granada following a kick in the groin and he then went off at the interval with a calf injury.
"He isn't available because he hasn't been able to train this week," coach Carlo Ancelotti told a news conference on Saturday.
"He'll return to training on Sunday and will be ready for the game on Wednesday," added the Italian referring to the King's Cup tie with Atletico Madrid.
"He doesn't need to do a lot of preparation as it is only a small problem. He needs to train and build up confidence."
The injuries to Bale have opened the door to youth product Jese who impressed again in the second half against Granada.
"I can play Jese or Angel Di Maria in his place, we will see. Jese's position in the squad is clear and he doesn't need to win anybody over - we are all happy with what he is doing," said Ancelotti.
Third-placed Real are one point behind Barcelona and Atletico Madrid after a run of five straight wins but face a tough game at Athletic who have yet to lose at San Mames this season.
"They are a strong team and playing well. They play football at a high tempo. (Coach Ernesto) Valverde is doing a very good job there but if we play at our best we will win," said Ancelotti.
"It is very important to win. During January we are showing our quality and everyone needs to keep going at the same level."
(Editing by Tony Jimenez)
