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.
"Give us our money we do not want to beg. You and your children are playing with this money," he said about Saudi's oil wealth in the 30-second video during which he held up his identification card.
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."
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".
"Please listen to us. We want housing, we want a decent life," he said, apparently addressing Saudi authorities.
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.
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.
Saudis, complaining their salaries are not enough to make ends meet, are increasingly taking to Twitter and other social media to demand better living conditions.
Despite its huge oil wealth, Saudi Arabia has a jobless rate of more than 12.5 percent among its native population.
President Obama met a campaigner for the rights of woman in the ultra-conservative Muslim kingdom before leaving, after a short visit aimed at smoothing over policy differences with Washington's longtime ally.
The exclusion of concerns over women's rights and religious freedoms drew criticism from international watchdogs and from activists inside the kingdom.