STORY: The vote is being held on the anniversary of Saied's sudden move against the elected parliament when he ousted the government, established emergency rule and began governing by fiat.
It is not clear when the results will be announced after polls close at 2100 GMT, but with little apparent enthusiasm for the vote among most Tunisians and a boycott by major parties, analysts expect a 'yes' vote with low turnout.
"People against the vote don’t want to serve the country they have special interests, they do not care about the country, they care about their own interests, this is why they are against the referendum, this new constitution foretelling a great future for Tunisia," said voter, Mouhamed Ali Chabouhi.
Under Saied's own rules for the referendum, no minimum level of participation is needed to approve the new constitution. They only stipulate it will come into effect once the final results are published, and do not say what happens if voters reject it.
Saied has hailed his moves as the foundation of a new Tunisian republic to put the revolution back on course and end years of political sclerosis and economic stagnation.
His foes accuse him of a coup.
Most Tunisians remain focused on the dire economy and rising prices.
The economic decline in Tunisia since 2011 has left many people angry at the parties that have governed since the revolution and disillusioned with the political system they ran.
A turnout on Monday far below that rate would further call into question the legitimacy of Saied's new constitution and his project to remake Tunisian politics.