Bale has been struggling with injury since he arrived in the Spanish capital following his world-record transfer from Tottenham, and has appeared in just two league games so far.
He had already been ruled out of Wednesday's Champions League clash with FC Copenhagen but this latest diagnosis suggests a longer absence.
"After the tests carried out today, the player Gareth Bale has been diagnosed with a muscle contracture in his left thigh," said a statement on the Real Madrid website.
"It remains to be seen how the condition develops."
He is likely to 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.