The lawyers were convicted, among other charges, of "disobeying the ruler" as well as undermining and slandering the judicial system which they described as "retarded," it said.
They used "Tweets on social media" to carry out the offences, said SPA.
"All this is to undermine public order," the agency reported, without identifying the accused or giving further details about what they wrote.
The court sentenced one accused to eight years in prison, while the other two were handed five-year terms.
The sentences start from the dates of their arrest, which were not specified.
They will also be banned from travel for several years and "from appearing in the media or writing in it, and through social media whatsoever, even under different IDs/names," SPA said.
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The court warned that social media users in Saudi Arabia were being monitored and would be treated the same way as the lawyers.
In February, media watchdog Reporters Without Borders (RSF) said that Gulf monarchies, fearful of unrest, have stepped up efforts to monitor and control the media, particularly online.
Saudi Arabia, which is on the group's "Enemies of the Internet" list, has been particularly aggressive in policing the Internet, including by arresting those who post critical articles or comments, RSF said.
In early March, a Saudi court jailed a Tweeter for 10 years after convicting him of insulting the kingdom's political and religious leaders and urging anti-regime protests, state media said.