Their Facebook campaign, dubbed Women2drive, says the action will start on Friday and keep going "until a royal decree allowing women to drive is issued" in the ultra-conservative kingdom -- the only country where women face such a ban.
Saudi Arabia has been largely spared the spillover effect of uprisings across the Arab world, after two calls for protests in March went unanswered.
But now "it seems that women, who are the main victims of suppression, will carry the banner of change in the Saudi society," said columnist and novelist Badriya al-Bishr.
There is no law banning women from driving in the oil-rich kingdom, but the interior ministry imposes regulations based on a religious edict stipulating women should not be permitted to drive.
Women in Saudi Arabia face a plethora of constraints, ranging from having to cover from head to toe in public, and needing authorisation from a male guardian to travel, to having restricted access to jobs due to strict rules of segregation.
Due to the ban, women end up having to hire foreign drivers whose wages eat into their salaries. If they cannot afford a driver, they have to rely on male members of their immediate families to give them a lift.
"The political leadership should take a decision to allow women to drive," said Bishr. "The Saudi society has changed. Sixty percent of the people are young who are ready to live in a modern way," she said.
Authorities cite vehement objection by conservatives to letting women operate their own vehicles, as evidenced by a counter-campaign on Facebook that urged men to "beat" their women if they spot them breaking the ban on June 17.
But conservatives have always rejected measures embracing aspects of modernity that they deem conflict with tradition.
"The introduction of radio, television, and schools for girls have all faced opposition from society in the past, but were imposed by royal decrees," said one activist requesting anonymity.
Some women did not wait for the date set for the protest and took to the road, and they have since paid the price.
Manal Al-Sherif, a 32-year-old mother, found herself behind bars for two weeks last month after defying the ban more than once and posting a video on the Internet showing her driving around Eastern Province.
King Abdullah was petitioned by some 3,345 people to intervene on her behalf, while some 24,000 people expressed support on a Facebook page set up to call for her release.
Sharif's action came a few days after another Saudi woman, Najla al-Hariri, drove in the western region of Jeddah over a few days, insisting on her right to drive.
Six other women were detained for hours last week after being caught learning to drive in an empty plot in north Riyadh. They were released after their male guardians were called in by police and signed pledges not to drive.
A group of women defied the ban in November 1990, stunning Saudi men by driving around Riyadh in 15 cars before being arrested.
The 47 women who took part in that protest were severely punished, with authorities suspending many from public sector jobs and reprimanding their male guardians.
In 2008, activist Wajiha Huwaidar posted a video on YouTube showing her driving in Eastern Province. She escaped arrest by not bumping into a police patrol.
Activists this time insist they are not planning a demonstration. The call is for women to act individually, wherever they are.
In a series of instructions posted on Facebook, organisers called on participants to raise the Saudi flag and posters of King Abdullah. They are also requested to make sure they wear the Islamic veil.
Among the advice is to have a male guardian, known as "Mahram."
"If you get arrested, do not be scared. You will only be asked to sign a pledge" not to drive, the recommendations said.