Prosecutors described the Paralympic athlete’s punishment for killing his girlfriend Reeva Steenkamp in 2013 as “shockingly lenient”.
At the hearing in Pretoria, Judge Thokozile Masipa said the petition had no reasonable prospect of success.
The state now has 21 days to take its case to the Supreme Court of Appeal.
Pistorius, 29, was given a five-year term for manslaughter in 2014, but was found guilty of murder last December after a prosecution appeal.
He shot Ms Steenkamp through a locked toilet door and said in his his defence that he mistook her for an intruder.
The judge said at the sentencing that she had deviated from the minimum 15-year sentence because of “compelling personal circumstances”.
She said mitigating circumstances, such as rehabilitation and remorse, had outweighed aggravating factors, such as his failure to fire a warning shot.