Polls opened in Cairo, Alexandria and eight other provinces and are scheduled to close at 7:00 pm in the first round. The rest of the country votes on December 22.
Alexandria, the country's second largest city, was the scene of clashes on the eve of the referendum between opponents of the draft charter and Islamists after a cleric told worshippers at a mosque to support the constitution.
Hundreds of protesters later laid siege to the mosque, where the cleric took refuge.
The charter is at the heart of a power struggle between President Mohamed Morsi and the opposition, backed by judges who accuse the Islamists of overreaching.
Weeks of protests preceded Saturday's vote, sparking clashes by rival camps in Cairo last week that left eight people dead and hundreds injured.
The vote will be staggered over two rounds to ensure there will be enough judges to monitor polling stations amid a rift within the judiciary over the referendum process.
The first round's unofficial results are expected hours after polling stations close.
Morsi has ordered Egypt's military to help police maintain security until the results are known. A total of 130,000 police and 120,000 soldiers are being deployed, interior ministry and military officials told AFP.
Morsi's Muslim Brotherhood has organised large rallies and a campaign in favour of the draft constitution.
The main opposition coalition, the National Salvation Front, mulled a boycott before instead urging Egyptians to vote against the charter, which rights groups say limits the freedoms of minorities and women.
In a small queue at a Cairo school serving as a polling station, watched over by police and soldiers, several people said they were voting against the constitution.
"I'm voting because I hate the Muslim Brotherhood, it's very simple. They are liars," said one, Abbas Abdelaziz, a 57-year-old accountant.
Ali Mohammed Ali, an unemployed 65-year-old wearing a traditional long robe, said: "I voted for Morsi and it was a mistake, a big mistake. This constitution is bad, especially because it doesn't forbid child labour and opens the way for the marriage of minors."
He, too, was against the Muslim Brotherhood and the fact that "prices have risen."
Other were in favour of the proposed charter.
Enayat Sayyed Mostafa, a retired woman, said: "I'm voting for stability and for Dr Morsi's promised programme of renewal. I have gone over the text to compare it with what the opposition is saying, and what they say is false. It's a good constitution."
The referendum was only made possible after Morsi assumed sweeping powers that stripped a court of the right to annul the Islamist-dominated constituent assembly that drafted the charter, as some expected it to do earlier this month.
Morsi was forced to rescind his powers after mass protests outside his palace in northern Cairo led to the worst violence between the opposition and Islamists since his election in June.
International watchdogs, including the UN human rights chief, the United States and European Union, have expressed reservations about the draft because of loopholes that could be used to weaken human rights, including those of women, and the independence of the judiciary.
Analysts said the proven ability of the Muslim Brotherhood movement to muster voters was likely -- but not certain -- to ensure that the draft constitution is passed.