The ultra-conservative Islamic state has said it has the right to stop women revealing 'tempting' eyes in public.
A proposal to enshrine the measure in law has been tabled, Daily Mail reported Saturday quoting Sheikh Motlab al Nabet, spokesperson for Saudi Arabia's Committee for the Promotion of Virtue and the Prevention of Vice.
Women in Saudi Arabia already have to wear a long black cloak, called an abaya, cover their hair and, in some regions, conceal their faces while in public.
If they do not, they face punishment including fines and public floggings.
The proposal was made after a member of the committee was attracted by a woman's eyes as he walked along a street, provoking a fight, one report on the Bikya Masr news website suggested.
The woman was walking with her husband who ended up being stabbed twice in the hand after the altercation.
The virtue and vice committee has repeatedly been accused of human rights violations. Founded in 1940, its function is to ensure that Islamic laws are not broken in public in Saudi Arabia.
In 2002, the committee refused to allow female students out of a burning school in the holy city of Mecca because they were not wearing correct head cover. The decision is thought to have contributed to the high death toll of 15.
They are also banned from driving by religious edict and cannot travel without authorisation from their male guardians.