Bale, who became the world's most expensive player when he joined from Tottenham Hotspur for a fee of 100 million euros (£85m) in the close season, trained apart from his team mates in the gym on Tuesday, Real said on their website.
The Welshman had a scan on Wednesday morning but Real did not say how long Bale would be sidelined for.
He is, however, likely to also miss Saturday's La Liga game at Levante and may not be able to join up with Wales for their World Cup qualifiers at home to Macedonia on October 11 and away to Belgium four days later.
Bale made his home debut for the nine-times European champions when he came on at half time in Saturday's 1-0 derby defeat to Atletico Madrid.
He was due to play his first game at the Bernabeu against Getafe the previous weekend but was withdrawn from the starting line up after tweaking his thigh muscle in the warmup.
Real won their opening Champions League match 6-1 at Turkish side Galatasaray but have faltered in La Liga and Saturday's defeat left them five points behind champions Barcelona and Atletico, who both have a perfect 21 points from seven games.