The Welshman did not train with the rest of the Real squad on Tuesday after picking up the injury in training a fortnight ago.
Bale - who moved to the Bernabeu from Tottenham for a world-record fee in the close-season - struggled with back and thigh problems earlier in the season, but has notched seven times in 10 La Liga appearances in a promising start to his career in Spain.
Real returned to training on Sunday following time off for the mid-season break, but Bale had to train alone.
Centre-back Raphael Varane is also unavailable for selection on Thursday, with the Frenchman continuing to suffer with a knee injury.
Carlo Ancelotti's side return to Liga action against Celta Vigo on Monday.
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