Carl, who has supported his 27-year-old brother during his trial over the death of model Reeva Steenkamp, was involved in a head-on collision with another vehicle while on a motorway outside Modimolle, a town 80 miles north of Pretoria.
Hospital officials have said that Carl was admitted to intensive care, but is believed to be out of danger.
CLICK ON PHOTOS FOR FULL GALLERY
Carl Pistorius with his sister Aimee and father Henke
Reports suggest that Carl has broken his right arm, leg and left foot and has also injured his hip.
"Carl is badly hurt but out of danger," said Oscar and Carl's uncle Arnold Pistorius. "His vehicle was hit head-on by another car that had suddenly, and without warning, swerved."
"Carl was returning from a business trip to Polokwane," added the family statement. "A colleague was following in a separate vehicle and witnessed the collision. He was able to tell us what happened."
Carl has been supporting his brother Oscar in court
Police spokesperson Brigadier Hangwani Mulaudzi said Carl was travelling alone in a Toyota Corolla when the accident happened.
"Both drivers were trapped in their vehicles and had to be removed by emergency services using the jaws of life," he said.
Oscar's brother was previously involved in a car accident in 2008 which resulted in the death of a young woman. Carl was later cleared of the female motorcyclist's death.