Women must have the consent of a male guardian to travel abroad, and often need permission to work or study.
Support for the first large-scale campaign on the issue grew online in response to a trending Twitter hashtag.
Activist Aziza Al-Yousef told the BBC she felt “very proud” of the campaign, but now needed a response.
In the deeply conservative Islamic kingdom, a woman must have permission from her father, brother or other male relative – in the case of a widow, sometimes her son – to obtain a passport, marry or leave the country.
Many workplaces and universities also demand a guardian’s consent for female employees and students, although it is not legally required.
Renting a flat, undergoing hospital treatment or filing a legal claim often also require a male guardian’s permission, and there is very little recourse for women whose guardians abuse them or severely limit their freedom.
In July, an Arabic Twitter hashtag which translates as “Saudi women want to abolish the guardianship system” went viral after a Human Rights Watch reportwas published on the issue. Saudi women tweeted comments, videos and artwork calling for change. Bracelets saying “I Am My Own Guardian” appeared.
The women counted on the petition all gave their full names, though more signed anonymously. Hundreds of women – one estimate suggests as many as 2,500 – bombarded the Saudi King’s office over the weekend with telegrams containing personal messages backing the campaign.
Human Rights Watch researcher Kristine Beckerle, who worked on the report, described the response as “incredible and unprecedented”.
“I was flabbergasted – not only by the scale, but the creativity with which they’ve been doing it,” she said. “They’ve made undeniably clear they won’t stand to be treated as second-class citizens any longer, and it’s high time their government listened.”
However, there has been opposition from some Saudi women, with an alternative Arabic hashtag, which translates as #TheGuardianshipIsForHerNotAgainstHer, gaining some traction, and opinion articles, like this one on the Gulf News website, arguing that the system should be reformed and applied better.
Ms Yousef, who was stopped by police in 2013 for breaking the country’s ban on women driving, said she did not expect any negative consequences from the petition: “I’m not worried, I’m not doing anything wrong,” she said.
She and another activist took the petition to the Royal Court in person on Monday, but were advised to send it by mail.
She said a key demand is that an age between 18 and 21 be designated, above which a woman be “treated like an adult”.
“In every aspect, the important issue is to treat a woman as a full citizen,” she said.
She and other activists first raised the issue five years ago. “We never had a problem with campaigning, but the problem is there is no answer. But we always hope – without hope, you cannot work,” she said.
There has been no official response to the petition yet.