Carl Pistorius allegedly killed a woman motorcyclist while driving outside Johannesburg, the eNews Africa television channel and radio station Eyewitness News reported, citing his lawyer Kenny Oldwage.
His trial had been due to start last Thursday, a day before his famous brother, an Olympic and Paralympic hero, was granted bail on a charge of murder over the Valentine's Day killing of his girlfriend Reeva Steenkamp.
Carl Pistorius's trial was pushed back a month, but the specific date is not known.
He had been in court in Pretoria last week with his sister Aimee and father Henke to support his brother.
Oldwage, who also represents Oscar Pistorius, was not immediately reachable for comment.
Oscar Pistorius, the 26-year-old double amputee athlete known as "Blade Runner" was released on one million rand ($112,770) bail on Friday. He is due back in court on June 4.
He says the shooting of his 29-year-old model girlfriend was an accident and that he mistook her for a burglar.
The family's public relations managers said they would issue a statement later on Sunday.