The Paralympian athlete was sentenced in October for the culpable homicide of his girlfriend Reeva Steenkamp, whom he shot at their home last year.
Prosecutors called the five-year prison term "shockingly light", and said they would appeal for a tougher sentence.
They also vowed to appeal against Pistorius' acquittal on murder charges.
The double-amputee sprinter had been charged by the prosecution with the pre-meditated murder of Ms Steenkamp, a model and law graduate.
He was also acquitted of the lesser murder charge of dolus eventualis by High Court Judge Thokozile Masipa.
In South African law, this charge - also known as common-law murder - applies if the accused knew they might kill someone but still went ahead with their course of action.
Judge Masipa will rule on whether the prosecution's appeal is allowed to go ahead.
'Inappropriate'
In papers filed with the High Court last month, prosecutor Gerrie Nel said Judge Masipa had "erred in over-emphasising the personal circumstances of the accused".
"Not enough emphasis was placed on the horrendous manner in which the deceased died coupled with the gruesome injuries she sustained when the accused shot and killed her," he said.
Pistorius' sentence was "shockingly light, inappropriate and would not have been imposed by any reasonable court", Mr Nel argued.
The judge, he said, had failed to sufficiently consider that Pistorius had fired four shots "through a locked door into a small toilet cubicle from which there was no room to escape".
The prosecution had called for the maximum 15-year sentence for culpable homicide, or manslaughter.
Ms Steenkamp was killed at Pistorius' home in Pretoria in the early hours of Valentine's Day last year. He said he feared there was an intruder but he did not intend to kill.
Pistorius is serving the sentence in the hospital wing of Pretoria's Kgosi Mampuru II prison.
He can apply to serve the rest of his sentence under house arrest after 10 months in prison.
(BBC)
ANN.Az
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