The performance company issued a statement Saturday saying the male artist was appearing in the "Wheel of Death" act during the 7 p.m. performance of Zarkana when he slipped and fell off the wheel.
The act features two people who perform high-risk feats atop and inside a pair of spinning wheels rotating high above the stage, including rope skipping and jumps.
The company says the show was halted and the performer was taken to University Medical Center, where he was in stable condition and expected to be discharged in the next few days.
The company says it has a policy of not releasing performer's names.
The accident occurred four months after a Cirque du Soleil acrobat died in a fall during a performance of the show Ka at the MGM Grand in Las Vegas.
On Tuesday, safety officials announced plans to cite Cirque du Soleil and the MGM after investigators concluded 31-year-old Sarah Guillot-Guyard fell 94 feet to the floor below on June 29 when a wire rope she was suspended from was severed due to her rapid ascent.
Guillot-Guyard was the first Cirque du Soleil performer to die in an onstage accident in the company's 29-year history.