After he was sentenced earlier this month, Pistorius' lawyers said the double-amputee Olympic sprinter would not appeal against the term, which was criticised by many activists as too short.
"The sentence of six years imprisonment, in all the circumstances, is disproportionate to the crime of murder committed (and) shockingly too lenient," the National Prosecuting Authority said in a strongly worded statement.
The NPA added that the sentence was "an injustice and has the potential to bring the administration of justice into disrepute", saying that it would file papers to apply for leave to appeal on Thursday.
At the sentencing, High Court judge Thokozile Masipa listed several mitigating factors for giving him to less than half the minimum 15-year term for murder, including the athlete's claim he believed he was shooting an intruder.
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"He cannot be at peace. I'm of the view that a long term of imprisonment will not serve justice," Masipa said.
Pistorius, 29, previously a role model for disabled people worldwide, is being held in Kgosi Mampuru II prison in Pretoria.
But an appeals court upgraded his conviction to murder in December.
At a hearing in June, Pistorius, sobbing heavily, hobbled on his stumps across the courtroom to demonstrate his physical vulnerability.
His lawyers had argued he should not be returned to jail on account of an anxiety disorder and depression.
Pistorius, who pleaded not guilty at his trial in 2014, has always denied killing Steenkamp in a rage, saying he was trying to protect her.
The year before he killed Steenkamp, Pistorius became the first double-amputee to race at Olympic level when he appeared at the London 2012 games.