Pistorius' lawyers said the Olympian would not appeal against the term, which was also criticised by many activists as too short.
High Court judge Thokozile Masipa listed several mitigating factors for sentencing him to less than half the minimum 15-year term for murder, including the athlete's claim he believed he was shooting an intruder.
"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 (NPA) 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", adding that it would file papers to apply for leave to appeal on Thursday.
Pistorius shot Ms Steenkamp in the early hours of 14 February 2013, saying he mistook her for a burglar when he fired four times through the door of his bedroom toilet.
The 29-year-old is being held in Kgosi Mampuru II prison in Pretoria.
He was released from the same jail last October after serving one year of a five-year term for culpable homicide - the equivalent of manslaughter.
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.
Ms Steenkamp's family said in a statement that they had "no input in the decision of the state to appeal" and are focusing their energy on the launch of a foundation in her name next month.
Sky News.
