The petition says that Saudi women, who are being treated as legal minors based on an interpretation of the Quran, must have the right to move freely around the country and abroad, as well as make important decisions regarding their own lives, without asking a man's permission.
"In every aspect, the important issue is to treat a woman as a full citizen," Saudi human rights campaigner Aziza Yousef told BBC.
Currently, women in Saudi Arabia are required to obtain approval from a male relative to make decisions regarding such daily social issues as medical treatment and employment. Before marriage it is usually a woman's father who exerts control. After the ceremony is completed responsibility is administered by the husband.
Sheik Abdulaziz al-Sheik condemned the request, calling the Twitter campaign anti-Islamic, and declaring that such actions threaten the wellbeing of Saudi society.
"This is an evil call that goes against the sharia and the instructions of the prophet," he blustered, cited by Middle East Eye.
Though Saudi UN representatives have pledged to the UN Human Rights Commission that the system will be dismantled, nothing has been done.
The unprecedented petition is the result of a social media campaign which began after Human Rights Watch published a report in July condemning the male guardianship system as a violation of human rights. No response to the petition has been recorded.