The new charter aims to replace the constitution passed under Islamist President Mohammed Morsi months before he was ousted by the army.
BBC reports that the military wants a strong “Yes” vote to endorse Mr. Morsi’s removal.
His Muslim Brotherhood, now designated a terrorist group, is boycotting the vote and there are fears of violence.
Shortly before voting began, an explosion took place near a court building in Cairo’s Imbaba district, although no casualties were reported.
A huge security operation is being mounted for the two days of voting. The interior ministry said 200,000 police officers, 150 central security units and 200 combat groups are being deployed around polling stations on both days.
Army chief Gen. Abdel Fattah al-Sisi visited one polling station in north Cairo, telling guards there: “Work hard. We need the referendum to be completely secured.”
The BBC says this has been a distorted campaign, with endorsements for the new constitution flooding state-run and private TV and radio.
However, spotting any posters from the No campaign is a lot harder and people have been arrested for putting them up.