The world's most expensive player had been due to make his Bernabeu bow in Sunday night's clash with Getafe but felt a tweak in his left thigh during the warm-up and was left out by coach Carlo Ancelotti as a precaution.
Bale underwent further tests on Monday morning at the Sanitas hospital in La Moraleja where, according to a medical statement from the club, it was confirmed that the Wales international was suffering from muscle fatigue.
The statement on www.realmadrid.com read: "After the tests carried out today on Gareth Bale at the Sanitas La Moraleja hospital, fatigue in the left thigh muscle was found. It will be treated."
It is not known when the 100million euro signing from Tottenham will be available to make his third Madrid appearance but reports in Spain suggest that while he will miss Wednesday's trip to Elche, he could be fit to face Atletico on Saturday.
Ancelotti felt that could be the case following Madrid's 4-1 win over Getafe.
"It is difficult to recover in three days, I am sure he will be ready for the game on Saturday," said the Italian.
"Today he had a small problem and we hope it is resolved quickly."
He added in the post-match press conference: "He is very upset at the moment because he was desperate to play his first game at the Bernabeu.
"I don't think it is a big problem, we have to wait until tomorrow to do a scan to see how bad the injury is.
"He wasn't comfortable, he was worried and so it was better to avoid problems."
The 24-year-old Bale only played 45 minutes in pre-season with Tottenham prior to his record-breaking move to Madrid, plus half an hour for Wales in a World Cup qualifier against Serbia.
He then played 60 minutes on his Madrid debut against Villarreal last week, where he scored his side's opening goal in a 2-2 draw, and also featured as a second-half substitute in the midweek Champions League win at Galatasaray.