The new charter aims to replace the constitution passed under former president Mohammed Morsi months before he was deposed by the army in July 2013 after nationwide protests against his Islamist rooted regime.
The two-day voting is also the first test for the army-backed coup that ousted Morsi and his Muslim Brotherhood, which has since been designated a terrorist group. The Brotherhood has called for a boycott of the polls.
A huge security operation is being mounted amid fears of violence. The Interior Ministry says 200,000 police officers, 150 central security units and 200 combat groups are being deployed around polling stations on both days of voting.
Shortly before voting began, an explosion was heard near a court building in Cairo, although no casualties were reported.
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Morsi supporters have said they would stage massive demonstrations and have labelled the draft charter a "constitution of blood". In response, the government has warned it would deal harshly with anyone interfering with the referendum.
But it also gives the military special status by allowing it to select its own candidate for the job of defence minister for the next eight years and empowering it to bring civilians before military tribunals.
The "yes" vote could also pave the way for fresh presidential and parliamentary elections. It would also provide a popular mandate for the military chief el-Sissi to run for president in elections later this year.