The vote on the constitution has the backing of minorities but supporters of ousted former President Mohammed Morsi said the poll moves Egypt further away from democracy.
The vote will test the popularity of Army Chief Abdul Fattah al-Sisi, who came to power after toppling Mr Morsi in July.
Supporters of the Muslim Brotherhood said the referendum is a sham, and acts to legitimise military rule.
"We had a transparent election which was held under international monitors," Brotherhood supporter Magdy Ouf said.
"And it was blown away."
"It is impossible to say that now there is democracy or a fair referendum."
But Magdy Abdel Baset, a supporter of General al-Sisi, disagreed.
"I will vote yes for the constitution for many reasons," he said.
"And the most important reason is to end the divisions among Egyptian people."
The referendum has polarised the Egyptian community in Australia, too.
Egyptian Australia William Boctor told SBS he voted in favour of a new constitution earlier this month.
He said it protects minorities by separating church and state.
General al-Sisi has deployed security forces to keep the peace at polling stations when Egyptians vote later this week.
