Four boys were hurt seriously enough to be transported to a hospital, KTLA-TV reported.
Preston Carter, who said he will be 101 next month, said he was backing out of a supermarket parking lot when the brakes gave way, police said. But some witnesses said they believed Carter hit the gas because he was frustrated children were in his way.
The incident occurred around 2:30 p.m. at Main Street Elementary School in south Los Angeles.
Carter's family said he was driving with a valid license but will not be getting behind the wheel again, whatever the investigation determines.