Prison officials told City Press newspaper that the athlete, who is serving a six-year sentence for murdering his girlfriend, was under 24-hour monitoring, with increased cell visits by warders.
Some inside sources told the paper that razor blades were found in the disgraced athlete's cell last Saturday afternoon, and that his wrist injuries, described as "severe", were self-inflicted.
Prison authorities have launched a probe into the incident.
"Our internal investigation is at an advanced stage," said Correctional Services spokesman Singabakho Nxumalo.
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According to the newspaper, the injury occurred soon after he had an altercation with prison officials over medication prescribed by state doctors. The Paralympian had refused to take the medication, saying it was "toxic" and demanded to be given medication prescribed by his private doctor.
He alleged that the prison official wanted to kill him and demanded to be transferred to another jail.
Warders also raided his cell and found a pair a scissors, prescription drugs and "toxic pills".
Pistorius initially escaped a murder conviction for shooting his girlfriend Reeva Steenkamp through a locked bathroom door three years ago.
An appeal by prosecutors saw his manslaughter conviction upgraded to murder, and in July he was sentenced to a six-year jail term.
But prosecutors have said they would push for a longer sentence, saying six years was "shockingly lenient".
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