It argued Judge Thokozile Masipa should have used the prescribed minimum 15-year sentence for murder as a starting point.
On September 18, National Prosecuting Authority (NPA) spokesperson Luvuyo Mfaku confirmed the date for the hearing.
Pistorius was imprisoned in July previous year after being found guilty on appeal of murdering his girlfriend Reeva Steenkamp on Valentine's Day 2013.
Pistorius was re-sentenced a year ago after prosecutors successfully argued that his conviction should be upgraded from culpable homicide to murder.
"It is shockingly lenient and has accordingly resulted in an injustice", she said, referring to the sentence. He was resentenced after the SCA in December 2015 held that he was indeed guilty of murder and not culpable homicide.
Prosecutors were asking the Supreme Court for permission to appeal against Pistorius's sentence after Judge Masipa denied them permission.
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Barry Roux, the lawyer who appeared for Mr Pistorius, told the court his client "had no intention to kill Reeva Steenkamp willingly and intentionally as he believed she was an intruder".
The Paralympic athlete shot Reeva Steenkamp dead on Valentine's Day in 2013, when he fired four times through the door of his toilet - an act, he says, that came from mistaking her for a burglar.
Judges can deviate from prescribed minimum sentences if there are compelling circumstances. The prosecution says there were no compelling reasons for Judge Masipa to give Pistorius a lighter sentence.
Ms Johnson called the six-year sentence "unjust", adding: "What we are saying is the court exercised its discretion inappropriately".
He had his legs amputated below the knee as a baby.
'Of course his disability is mentioned, but it can't not be mentioned, ' defence lawyer Kelly Phelps said. We know the disability is pervasive.