The defendant, who was not identified, had been convicted of inciting "families of those arrested for security reasons to protest by publishing Tweets and videos on YouTube," justice ministry spokesman Fahd al-Bakran was quoted by SPA as saying.
Prosecutors also found the defendant guilty of "mocking" King Abdullah, Saudi scholars and the judiciary, as well as criticising security services for arresting "promoters of extremist ideology".
In addition to the jail sentence, the court banned the defendant from travelling for eight years and posting on social media.
Security forces had previously arrested the accused on similar charges, but freed them after they signed a pledge not to take part in such activities again.
The sentence came two days after the Saudi interior ministry published a list of "terror" groups including the Muslim Brotherhood, Al-Nusra Front, which is Al-Qaeda's official Syrian affiliate, and the Islamic State of Iraq and the Levant, another jihadist group fighting in Syria and Iraq.
Saudi Arabia's interior ministry has said it will prosecute those who back such groups "financially or morally", or seek to promote them in the media and on social networks.
It also forbids "participation in, calling for, or incitement to fighting in conflict zones in other countries" as well as calling for demonstrations or taking part in them.
Last month, King Abdullah announced courts would issue jail terms of up to 20 years for anyone belonging to "terrorist groups" and fighting abroad.
Scores of Saudis are believed to have joined Islamist extremists fighting in Syria.
Saudi officials have issued stern warnings against volunteers from the conservative Sunni Muslim kingdom heading to fight alongside the mainly Sunni rebels battling Syrian President Bashar al-Assad's forces.
Riyadh established terrorism courts in 2011 to try dozens of Saudi nationals and foreigners accused of belonging to Al-Qaeda or of involvement in the wave of bloody attacks that swept the country from 2003.