Renzi, who has vowed to quit if he loses, was counting on a last-minute turnaround in voter sentiment to win backing for his proposals to streamline parliament and centralise some powers currently held at regional level in the name of more effective and stable government.
"Have you decided how you are going to vote, prime minister?" a female voter cheekily asked Renzi as he turned up at a voting station in his home town of Pontassieve near Florence.
Opposition parties have denounced the proposed amendments to the 68-year-old constitution as ill-considered and dangerous for democracy because they remove important checks and balances on executive power.
Spearheaded by the populist Five Star Movement, the biggest rival to Renzi's Democratic party, the No campaign has also sought to capitalise on the Renzi's declining popularity, a sluggish economy and the problems caused by tens of thousands of migrants arriving in Italy.
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"God willing it's over. A new era starts tomorrow I hope," said Matteo Salvini, leader of the far-right Northern League, after voting in Milan.
By midday nearly one in five of the 47 million Italians entitled to vote today had cast their ballot.
Polls close at 11.00 PM (local time) with the result, anxiously awaited across Europe, expected in the early hours of Monday.
If Renzi goes, some short-term market turbulence is inevitable. Some analysts fear a deeper crisis of investor confidence that could derail a rescue scheme for Italy's most indebted banks, triggering a wider financial crisis across the eurozone.
"If we miss this chance it won't come back for 20 years," Renzi warned voters before campaigning was suspended at midnight on Friday.
Voters have spent weeks passionately debating the pros and cons of the proposed reforms.
Polls have been banned since November 18. Up until then the "No" camp was leading comfortably -- but with a quarter of the electorate undecided.
After the Brexit vote and Donald Trump's victory, populism has been a factor, and Five Star, led by comic Beppe Grillo, would see a "No" vote as its stepping stone to government.