The former Tottenham man had been included in the starting line-up to face Getafe at the Bernabeu but was forced to pull out at the last minute after sustaining the injury to his left leg while taking practice shots at goal.
"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 [Monday] 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
Ancelotti all but ruled the forward out of Madrid's league game at Elche on Wednesday, but was confident he could face Diego Simeone's side at the Bernabeu, adding: "It is difficult to recover in three days, I am sure he will be ready for the game on Saturday.
"Today [Sunday] he had a small problem and we hope it is resolved quickly."
However, the Italian appeared concerned about Bale's fitness.
The 24-year-old only played 45 minutes in pre-season with Tottenham, plus half an hour for Wales in a World Cup qualifier against Serbia, and the 60 minutes he played on his debut against Villarreal last week, where he scored Madrid's opening goal in a 2-2 draw.
Asked if the fact Bale barely had a pre-season would affect him, Ancelotti responded: "I think so, the pre-season of Bale was very particular. Not only physically, but mentally too. He was waiting for a long time and I think this is a problem.
"Obviously we played him for just 60 minutes in Villarreal in order to protect him."
A Madrid statement 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."