At least five people were killed in confrontations between Muslim Brotherhood supporters and police, as Egypt went to the polls.
Polling stations closed after 12 hours of voting on a draft constitution that may set the stage for a presidential bid by army chief General Abdel Fattah al-Sisi.
The vote was the first since the military toppled president Mohamed Mursi.
The Brotherhood, backing Mr Mursi who is now in prison, has called for a boycott and protests over the draft which deletes Islamist language written into the basic law approved a year ago under Mursi. It also strengthens state institutions that defied him: the army, the police and the judiciary.
The referendum is a milestone in the political transition plan the army-backed government has been implementing while pressing a fierce crackdown on the Muslim Brotherhood, Egypt's best organised party until last year.
A presidential election could follow as soon as April.
Echoing a view widely held in Egypt, a senior European diplomat said Mr Sisi would probably announce his candidacy in the next few days - a prospect that will delight supporters but could stir more conflict with his Islamic opponents.
With little or no sign of a campaign against the draft - one moderate party says its activists were arrested while campaigning for a no-vote - it is expected to pass easily, backed by many Egyptians who staged mass protests on 30 June against Mr Mursi and the Brotherhood before his removal.
Others cited a desire to bring stability to Egypt after three years of turmoil ignited by the historic uprising that felled veteran autocrat President Hosni Mubarak in 2011.
Mr Sisi ousted Mursi, Egypt's first freely elected head of state, in July. His Islamist opponents say he is the mastermind of a coup that kindled the worst internal strife in Egypt's modern history and revived an oppressive police state.
Many are weary of the upheaval that has gripped this nation of 85 million and shattered its economy. They view Sisi, 59, as someone who can stabilise the country.
A Sisi presidency would mark a return to the days when the post was controlled by army men - a pattern broken by Mr Mursi's one year in office.