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 said the sentence was "an injustice and has the potential to bring the administration of justice into disrepute", saying it would file papers to apply for leave to appeal today.
At his sentencing, High Court judge Thokozile Masipa listed 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.
"He cannot be at peace. I'm of the view that a long term of imprisonment will not serve justice," said Masipa who was also the judge who had originally convicted him of the lesser charge of culpable homicide, equivalent of manslaughter.
Pistorius, 29, previously a role model for disabled people worldwide, is being held in Kgosi Mampuru II prison in Pretoria.
He was released from jail last October after serving one year of a five-year term for culpable homicide. But an appeals court upgraded his conviction to murder in December.
At a sentencing hearing in June, a sobbing Pistorius hobbled on his stumps across the courtroom to demonstrate his physical vulnerability.
But Steenkamp's father Barry told the court that he wanted Pistorius to "pay for his crime" of murdering Reeva.
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 Supreme Court of Appeal last year ruled he was guilty of murder, irrespective of who was behind the door when he opened fire with a high-calibre pistol he kept under his bed.
Barry Steenkamp and his wife June issued a statement on the latest twist in the long legal case, saying they "always fully supported (prosecutor) Gerrie Nel and his team's fight for justice".
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