Men and women gathered outside the Shura Council, the upper house of parliament where the Constituent Assembly drafting the charter meet.
"Women's voices are not heard in the constituent assembly!" read one sign held up by a protester.
The process of drafting a new constitution following an uprising that toppled president Hosni Mubarak last year has been widely criticised for being shrouded in secrecy.
But proposed articles have been leaked to the press which point to tussle between Islamists, who dominate the panel, and secularists over how much over a role religion would play in the charter.
Article 36 has been a particular concern for women's rights activists. According to leaks, it seeks to lower the age of marriage from 18, legalise female genital mutilation and use Islamic jurisprudence in a way that could limit women's rights to work and education.
"This constitution, especially article 36... is dangerous for women's rights," said political activist Inas Mekkawi, one of the organisers of Tuesday's demonstration.
"All the leaked articles are terrifying. There is no basis for equal citizenship rights for men and women " said protester Sabah Fawwaz Ibrahim, who wears the Islamic headscarf but says she does not belong to any organised party or group.
"The constitution is being written behind closed doors. They will write it and then go to the mosques and tell people to vote yes" in a referendum on the constitution, she told AFP.
The 100-strong panel, which was picked in June, is headed by senior judge Hossam al-Ghariani. Its constitutionality is currently being examined by a court.
A first Islamist-dominated Constituent Assembly was dissolved in April after a court found that it did not represent all Egyptians.
The military council that took power after Mubarak was toppled had suspended the constitution a day after the strongman fell in February 2011.
Egyptian women shout political slogans during a demonstration in Cairo in March 2012 (AFP/File, Mohammed Hossam)