The protests, dubbed the 15 September Movement, are set to take place on Friday after people gather in mosques around the country for the weekly congregational prayers.
A Twitter page set up for the movement says the aim of the protests is to urge authorities to address a range of issues including poverty, youth unemployment, housing crisis, increasing women's rights and releasing political prisoners.
"The movement represents every citizen who is gravely concerned about his homeland and thinks its sovereignty is under the control of the United Arab Emirates and Egypt and that his dignity has been trampled on by (US President) Trump," a statement for the group says.
"It represents everyone worried about the country's resources and thinks they are squandered in the pockets of a small class of people," the statement adds, a likely reference to the Al Saud ruling family.
The movement had received the backing of exiled Saudi dissident Ghanem al-Dosari and anonymous whistleblower Mujtahid, who tweets about the inner secrets of Riyadh's royal court.
Saudis have taken to social media to discuss the calls for public demonstrations with many hailing the move.
The calls for protests come amid an apparent a crackdown on critics of the country's foreign and domestic policies.
On Monday, activists reported on social media that the Saudi authorities had detained more than 20 Muslim preachers and scholars for unspecified reasons.
Prominent clerics Salman al-Awdah, Awad al-Qarni and Ali al-Omary were detained over the weekend, according to Saudi sources.
On Tuesday, activists dedicated to monitoring and documenting what they describe as “prisoners of conscience” reported that at least eight other prominent figures, including clerics, academics, television anchors and a poet, had been “confirmed” detained since Monday.
ALQST, a London-based Saudi rights group, also reported more arrests, including several of the same people, although it gave no specific figure.
“Al-Oudah, al-Qarni, Farhan al-Malki and Mostafa Hassan (are confirmed),” said Yahya al-Assiri, the center’s head, referring to four of those reported to have been arrested. “The rest are also correct, but I don’t have any specific information,” he added.
Al-Oudah and al-Qarni – who also supports a reconciliation with Qatar – are both known to be critical of the Saudi regime. Al-Oudah, who has more than 14 million Twitter followers, was jailed in the 1990s.
State news agency SPA said earlier on Tuesday that authorities had uncovered “intelligence activities for the benefit of foreign parties” by a group of people it did not identify.
The Doha-based International Union of Muslim Scholars has condemned the reported arrest of Muslim preachers and scholars in Saudi Arabia, urging Saudi King Salman to order their release.
The political upheavals in Saudi Arabia come while there are unconfirmed reports that King Salman plans to abdicate in favor of his son, crown prince Bin Salman. Such a move is likely to lead to royal infighting and increased dissent from clerics and social activists.