Activists say the document restricts freedom of speech and religion and limits women's rights.
Chair of the Islamist-dominated constituent assembly Hossam el-Ghiriani said the draft law, approved after a marathon session through Thursday night, would be sent to President Mohamed Morsi and a referendum would be held within two weeks.
The opposition, which has held daily protests since Morsi assumed broad powers in a decree last week, accuses the president and allies in the constituent assembly of railroading the charter through for a quick referendum.
Tens of thousands of demonstrators packed the square on Tuesday angered at Morsi's power grab and dozens have remained camped out ever since, with clashes in nearby streets between police and protesters erupting daily.
The constitution will replace the one suspended after president Hosni Mubarak's overthrow in early 2011.
Christians have objected to an article that seeks to narrow the meaning of "the principles of Islamic law" to the tenets of Sunni Muslim jurisprudence.
Heba Morayef, Human Rights Watch Egypt director, said some of the draft articles on freedom of expression and religion resemble a "penal code".
"Some of the provisions are penal code provisions. You don't list all the things that you are not allowed to do, you're supposed to set up the rights and limitations," she said.
Limits on religious freedom
Particularly worrisome was the limitation of religious freedom to followers of Abrahamic religions (Christianity, Islam and Judaism), Morayef said, which would exclude minorities such as Bahais that have been persecuted in Egypt.
"They have added language that is problematic to freedom of expression. You cannot 'insult a human', which is very broad. It can be used to censor criticism of the president," she said.
Several private newspapers announced that they would not appear on the street next Tuesday to protest what they consider to be a lack of press guarantees in the new charter.
Abdallah Sennawi, a member of the Committee to Defend Freedom of Expression and Thought, said private television channels would follow suit on Wednesday.
Morsi's decree, described by the opposition as dictatorial, stripped courts of the right to annul the controversial constituent assembly ahead of an expected court ruling on Sunday.
It shields Morsi's decisions from review by the judiciary, which he and his movement believe retains Mubarak-era appointees who are opposed to the Islamists.
The top Cassation Court has suspended work to protest the decree, which will expire once the constitution is ratified.
Morsi and his supporters argue that delaying the constitution, which would be followed by parliamentary elections to replace the Islamist-dominated house dissolved by a court earlier this year, would delay democratic transition.
In a pre-recorded interview broadcast on Thursday night, Morsi repeated that the new powers he had assumed were temporary.
"This is an exceptional stage; we are in a transitional phase," Morsi told state television. "This constitutional declaration is temporary, and it will end once the people have approved the constitution."
The Muslim Brotherhood said it plans to hold a pro-Morsi demonstration on Saturday, but that it will not be held in Tahrir Square to avoid any confrontation.
The assembly had announced on Wednesday it would vote on the charter the following day, to the shock of opposition groups holding out that Morsi would try to reconcile after Tuesday's nationwide protests.
Morsi allowed the assembly a further two months after its mid-December deadline to finish the charter, making the quick vote even more of a surprise to the opposition. – Sapa-AFP