Despite protests from rights groups, the three-day plebiscite is expected to approve sweeping constitutional changes that will extend Sisi's term until at least 2024 in the Arab world's largest state.
Beyond that, the amendments would allow Sisi, 64, to run for another six-year term while boosting his control over the judiciary and giving the military even greater influence in political life.
The referendum bucks the trend of the region's mini-Arab Spring, in which mass pro-democracy protests this month swept away veteran presidents in Algeria and Sudan.
Sisi made his grab for power in the turbulent years after the original Arab Spring protests of 2011 toppled long-time ruler Hosni Mubarak, who was followed in office by president Mohamed Morsi.
Egypt bucks trend with vote to extend Sisi rule
Sisi overthrew Morsi in 2013 and the following year won his first term as president. He was re-elected in March 2018 with more than 97 percent of the vote after standing virtually unopposed.
International observers slammed both elections while Sisi's government has been widely criticised for sweeping repression of its opponents -- both militants and secular groups.
Human Rights Watch charged the constitutional amendments aim to strengthen Sisi's "authoritarian rule", while Amnesty said that parliament, having already backed the changes, had shown a "complete disregard for human rights".
For the past few weeks, Egypt's streets have been awash in banners and billboards urging citizens to "do the right thing" and vote 'Yes', while popular folk singers have also exhorted voters to go to the ballot box.
Egypt sets referendum on extending Sisi's rule for April 20-22
A muted 'No' campaign mounted from the diaspora and online has been thoroughly muzzled as authorities have blocked over 30,000 internet domains.
Despite the deep concerns of rights groups, Sisi has earned the support of many Egyptians and some Western powers by presenting himself as a bulwark against Islamist militancy and turmoil at a time when fighting again rages in neighbouring Libya.
Many voters, such as retired banker Ramez Raouf, view Sisi as a champion of stability.
"Look, I am against a few of the changes such as extending the president's terms ... but I am still going to vote 'yes' anyway," Raouf, 63, told AFP.
When asked why, he said "because the military will protect the civilian nature of the state, and that's important to me".
Parliament has already voted overwhelmingly this week to approve the changes, including extending presidential terms from four to six years.
The referendum also proposes other changes to the five-year-old constitution, among them the creation of a second parliamentary chamber and a quota ensuring at least 25 per cent of MPs are women.
Think-tank the Soufan Center said the main effect of the referendum would be to "solidify Sisi's grip on the Egyptian political regime" in a country that "has become even more autocratic than it was under Mubarak".
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