Goal confirmed the adductor injury after Bale was replaced by Dani Ceballos in Saturday's 0-0 stalemate and suggested the 29-year-old could be a doubt for Tuesday's UEFA Champions League trip to CSKA Moscow.
Los Blancos currently sit at the top of Group G and can advance their Champions League efforts with a win in Russia's capital, although the loss of Bale would dent their hopes.
Bale endured another injury-hit 2017-18 term, as he was sidelined from late September for much of the remainder of the year with a calf injury.
However, he did return later in the campaign and proved his immense worth by netting twice in the UEFA Champions League final against Liverpool.
After the departure of Cristiano Ronaldo to Juventus in the summer, Bale became an even more crucial part of the side, and he has started 2018-19 in fine fashion, netting three goals and providing two assists in five matches.
In his various absences last term, Isco and Marco Asensio both showed terrific form and became key to Real's attack.
They can provide cover for Bale, but after Ronaldo's exit, the former Tottenham Hotspur man is now more important than ever at the Santiago Bernabeu.
Real manager Julen Lopetegui and the Los Blancos fans will be hoping he can return to fitness as soon as possible.