Oscar Pistorius, 27, was jailed for five years in October for shooting dead his girlfriend, Reeva Steenkamp, at his home on Valentine’s Day 2013.
Judge Thokozile Masipa said prosecutors could not challenge the length of the sentence given to Oscar Pistorius.
Oscar Pistorius’s lawyers had opposed the appeal request.
Prosecutors are seeking a murder conviction and the case will now go before South Africa’s Supreme Court of Appeal.
They have argued that Judge Thokozile Masipa misinterpreted the law when she ruled that Oscar Pistorius did not intentionally shoot Reeva Steenkamp.
Judge Thokozile Masipa Masipa announced the ruling in a Pretoria court on December 10.
“I cannot say… that the prospect of success at the Supreme Court of Appeal is remote,” she said.
“The application therefore in respect of count one is decided in favor of the applicant.
“The application for leave to appeal against the sentence is dismissed.”
Oscar Pistorius had been charged by the prosecution with the premeditated murder of Reeva Steenkamp, a model and law graduate.
He was also acquitted of the lesser murder charge of dolus eventualis – also known as common-law murder – by Judge Thokozile Masipa, who ruled that he did not intend to kill.
The prosecution had called for the maximum 15-year sentence for culpable homicide, or manslaughter.
Reeva Steenkamp was shot dead at Oscar Pistorius’ home in Pretoria in the early hours of Valentine’s Day last year. He said he feared there was an intruder.
Oscar Pistorius is serving the sentence in the hospital wing of Pretoria’s Kgosi Mampuru II prison.
Correspondents say the appeal is likely to take place in 2015.
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