The ride has metal arms, each with a seat at the end attached by a chain, that swing outward as the ride picks up speed. The arms rise and fall as they spin around a center pole, putting the seats horizontal to the ground.
The pole apparently collapsed, causing the arms to crash back toward the center, said Dennis Townsend, a chief in the Calaveras County unit of the California Department of Forestry and Fire Prevention.
The riders - mostly children - were hurt when their seats struck the ground or other parts of the machine, he said.
Three riders were airlifted to hospitals in Modesto and Sacramento, but the extent of the injuries was not immediately known, said Sgt. Dave Seawell, a spokesman for the Calaveras County Sheriff's Department.
Representatives from several area hospitals said they had treated teenagers for minor injuries including knee pain. Modesto Memorial North Hospital, where a victim was airlifted, said it was treating a patient who was in stable condition.
Authorities could not immediately determine what might have caused the accident, Townsend said.
The fair remained open but the carnival area was shut down, said Laurie Giannini, the fairground's marketing director. She said there were no fatalities.
The Calaveras County Fair and Jumping Frog Jubilee opened Wednesday and is held each year in late May. It was inspired by a Mark Twain story, "The Celebrated Jumping Frog of Calaveras County."
Last year's jumping frog contest drew 4,000 entries. This year's final is scheduled for Sunday.
The fairgrounds is located just outside the Gold Rush-era town of Angels Camp in the Sierra Nevada foothills. It bills itself as an "old-fashion county fair" with exhibits and a variety of entertainment.