Awad al-Qarni, previously accused of links to the banned Muslim Brotherhood, was also fined 100,000 riyals ($27,000), Okaz newspaper reported on its website late Thursday.
It did not name the "famous preacher" but Qarni himself confirmed the verdict on his @awadalqarni Twitter account late Thursday.
"I am prevented from writing" on the account, he wrote, before issuing a Twitter message early Friday thanking his followers.
Qarni was "one of the key clerics of the Sahwa movement," British scholar Toby Matthieson has written.
The Sahwa emerged in Saudi Arabia in the 1960s and 70s as "a modern form of Islamic activism" which had wide impact and whose founders were exiled Muslim Brothers, according to another expert, Stephane Lacroix.
Signup to our newsletter and follow us on Facebook and Twitter!
Saudi Arabia, Egypt and the United Arab Emirates have all declared the Muslim Brotherhood to be a "terrorist group".
Okaz said Riyadh's Specialised Criminal Court, which handles "terrorism" cases, convicted the preacher on Thursday of spreading content on Twitter which "could jeopardise public order and provoke public opinion."
It said the content "could affect the relationship of the people with the leadership, and the relationship of Saudi Arabia with other countries."
There were no further details but Okaz said Qarni was tried without having been arrested.
"We have appealed the case," Qarni said on Twitter.
Lacroix, of Sciences Po university in Paris, told AFP in December that changes late last year to the kingdom's highest religious authority confirmed an "anti-Sahwa, anti-Muslim Brotherhood" trend.
In 2010, Qarni was charged in absentia by an Egyptian court with funding the Muslim Brotherhood.