Prosecutors welcomed the decision, which could see the disgraced former Paralympian star sprinter receive a 15-year jail sentence.
"Our argument was that he should have been convicted of murder, and then would have been sentenced to a minimum sentence of 15 years. That is of course what we would like to happen," said the National Prosecuting Authority's Nathi Ncube.
Judge Thokozile Masipa, who was the original trial judge, said: "I cannot say ... That the prospect of success at the Supreme Court of Appeal is remote.
The Supreme Court of Appeal will now review Judge Masipa's application of the law during the trial and decide whether Pistorius is guilty of murder.
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Masipa refused leave to appeal against the five-year sentence for culpable homicide that she imposed on Pistorius.
"The application for leave to appeal against the sentence is dismissed."
If found guilty of murder, however, he would likely receive a much harsher sentence.
Pistorius said he shot Reeva Steenkamp four times through a locked toilet door on Valentine's Day 2013 in the belief she was an intruder.
Masipa found him guilty of culpable homicide, also known as manslaughter, and sentenced him to five years in jail, meaning that the 28-year-old could have ended up spending only 10 months of his jail term at Pretoria's central prison.
The athlete's father, Henke Pistorius, told AFP outside the court: "It should not have gone this far."
But, he added: "Oscar is strong, he's strong, he has to be strong, he grew up like that. There's lots of things in life, especially for a man like him that is... Not fair."
"There is an appeal, and that is a good thing," said Martin Hood, a criminal lawyer based in Johannesburg.
"A higher court can look at the case in its totality.
"If the conviction is changed to murder then obviously the sentence will fall away and there will be a new harsher sentence," said Hood.