The Wales international was set to make his Bernabeu bow following his world-record move from Tottenham over the summer but was forced to miss the 4-1 win over Getafe after hurting his left leg while taking practice shots at goal.
Bale will undergo tests on Monday but manager Carlo Ancelotti is hopeful he will recover to face rivals Atletico Madrid on Sunday, even if he misses a midweek trip to Elche.
"He is very upset at the moment because he was desperate to play his first game at the Bernabeu," said Ancelotti in his post-match press conference.
"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.
"It is difficult to recover in three days; I am sure he will be ready for the game on Saturday."
A Madrid statement later read: "Gareth Bale felt a tweak in his left thigh during the warm-up and as a precaution it was decided that he should not participate in the match against Getafe.
"The diagnosis is subject to further tests that will take place tomorrow in the Sanitas hospital in la Moreleja, Madrid."
Bale made his debut for Madrid in last weekend's 2-2 draw at Villarreal, getting on the scoresheet in the process.
He also came on as a substitute in the 6-1 thrashing of Galatasaray in the Champions League in midweek.