Those convicted include Sheikh Athbi Al-Fahad Al-Sabah, a nephew of the Gulf state's emir and the former head of the secret service police, according to an official court verdict.
He was one of three royals convicted, along with two other Kuwaiti citizens, of publishing posts on social media accusing judges of accepting bribes.
The five men were sentenced last year. An appeals court upheld the verdict in January.
The supreme court also upheld a one-year jail term for a sixth defendant and acquitted six others, according to the verdict.
The judge and the former prime minister have both denied the allegations.
A thirteenth defendant, who allegedly posted online the footage, was sentenced to 10 years in jail by a lower court. He did not appeal the challenge and has since left Kuwait, according to the verdict.