The arrests were made on Saturday, the day US President Barack Obama flew home from Saudi Arabia under fire for not having done more to raise human rights concerns during talks with King Abdullah, activists said.
In one video seen by AFP, a young man identifying himself as Abdulaziz Mohammed al-Dosari addressed King Abdullah saying he has to survive on a low income, and does not own a house or a car.
"We are fed up, and you still blame those who carry out bombings," the man says, urging the king to give Saudis money to improve their lives.
In another video, a man identifying himself as Abdullah bin Othman charged that "corruption is widespread" in Saudi Arabia while "people are hungry and oppressed."
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Othman urged other Saudis to go online and post their comments "so that our voices could reach the king".
In a third video, a man calling himself Saud al-Harbi said many of his compatriots are in need of "housing" and a "decent life".
And he added: "Do not force people to take to the streets."
Saudi Arabia is an absolute monarchy where protests are banned.
AFP could not immediately verify the authenticity of the videos nor confirm the arrests from official sources.
In February, media watchdog Reporters Without Borders (RSF) said that Gulf monarchies, fearful of Arab Spring-inspired 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.