The reforms would strengthen the hand of the prime minister against parliament and the president, while expanding the responsibilities of regional governments to include key areas such as tax and education.
Two hours before the close of polls on the first day, the interior ministry said about 10 million Italians had cast their ballots, or 22.4 percent of the country's 50 million registered voters.
The proposals were brought in by the previous centre-right government under Silvio Berlusconi, who continues to promote them despite losing April's election and taking a hammering in subsequent local polls.
Supporters say that after a history of no less than some 50 post-war governments, the reforms would provide greater political stability.
Opponents, including centre-left Prime Minister Romano Prodi, see them as an attack on the 1947 constitution, a hallowed text of Italian democracy after its fascist regime of World War II.
Critics fear in particular they could deepen the gulf between the economically prosperous north and the less prosperous south.
"Only the right wing has voted in favour of this reform which would re-write no less than 50 articles out of 139," warned Leopoldo Elia, a lawyer and prominent figure in a "Save the Constitution" movement.
"Above all it threatens national unity," he said, noting that reform would give the regions exclusive authority over their health and educational facilities.
The referendum went ahead after the proposed constitution changes failed to obtain the requisite two-thirds majority in parliament in November.
But coming so soon after the general and municipal elections this year, President Giorgio Napolitano made a special appeal for a large turnout, saying the issue went to the foundations of the republic.
The referendum, which will be valid whatever the turnout, covers reforms negotiated last year by Berlusconi, while he was still prime minister, with his small populist allies known as the Northern League, who threatened to quit his coalition if the changes were not introduced.
The Northern League sees the reforms as a first step toward federalisation including an entirely decentralised tax system.
Observers have also said the vote is another key test for the centre-right following its defeat in April, with the Il Sole 24 Ore daily saying the plebiscite is "the final duel between Prodi and Berlusconi".
Warning against change, Senator Andrea Manzella said: "The present constitution was born out of a long period of denial of freedom.
"It was also an expression of the (wartime Italian) resistance. But above all it symbolised wisdom at a moment of great confusion."
Opponents are also unmoved by the argument that stability would be enhanced by a stronger prime minister.