Jubeil made the announcement at a regional security summit in Bahrain, a day after Turkish prosecutors demanded the extradition of the 18 suspects to Turkey for trial.
"On the issue of extradition, the individuals are Saudi nationals. They're detained in Saudi Arabia, and the investigation is in Saudi Arabia, and they will be prosecuted in Saudi Arabia," he said.
The Saudi minister vowed that the government will bring those responsible for the murder to justice.
"We will hold people to account and those responsible will be punished, and we will put in place mechanism to make sure that it won't happen again," Jubeil noted.
Khashoggi, a columnist for US newspaper the Washington Post and a critic of the Saudi government, has been missing since his entry into the Saudi consulate in Turkey's Istanbul on October 2.
On October 20, Saudi Arabia said Khashoggi died in a "brawl" in the consulate, without explaining the cause of his death.
Saudi King Salman later ordered the re-organization of the intelligence authorities and sacked senior intelligence officials.
