The vote has been fiercely opposed by months of deadly street protests and criticized internationally.
Venezuela’s opposition says it is a bid for the beleaguered Maduro to cling to power by getting around the parliament controlled by its lawmakers.
State television showed Maduro voting in a west Caracas polling station for the 545-member citizens’ assembly that will be empowered to dissolve the opposition-controlled parliament and change laws as it reforms the nation’s charter.
Turnout will be key in the election. The opposition has urged a boycott, saying the vote was a move towards “dictatorship” with the backing of the military.
Surveys by the Datanalisis polling firm show more than 70 percent of Venezuelans opposed the idea of the new assembly — and 80 percent reject Maduro’s leadership.
Four months of street protests against Maduro have left more than 100 people dead, and exposed deep political divisions in this oil-rich nation reduced to economic calamity.
More demonstrations were called for Sunday’s vote, despite a ban Maduro has decreed threatening prison terms of up to 10 years for protesters.
But fear of the violence worsening has rippled across the region, and beyond.
The US, the EU and Latin American powers, including Argentina, Brazil, Colombia and Mexico, have come out against the election, saying it would destroy Venezuelan democracy.
Several foreign airlines, including Air France, Delta, Avianca and Iberia have suspended flights to the country over worries about security.
Families of US diplomats there have been ordered to leave following the imposition of American sanctions on 13 current and former Venezuelan officials.
Maduro — who described the Constituent Assembly as a “card that will win this game” — on Saturday said the vote was “the most important election held in Venezuela’s political system.”
Authorities on the eve of the vote said all was ready for the nationwide balloting, although the head of the electoral council acknowledged some voting machines had been burned in attacks on polling stations.
Freddy Guevara, an opposition lawmaker, said the new assembly was “fraudulent” and Maduro was “making the biggest historical mistake he could commit.”
The head of Datanalisis, Luis Vicente Leon, said the Constituent Assembly “wasn’t being formed to solve the country’s problems,” but was instead a political gambit because the uncharismatic Maduro — whose term is meant to finish next year — “can’t win elections.”
Colombia and Panama — refuges for tens of thousands of Venezuelans fleeing the chaos at home — have said they will not recognize the results of Sunday’s election in Venezuela.
At an overnight protest in Villa del Rosario, a Colombian town on the Venezuelan border, hundreds of Venezuelans taking shelter there decried the election.
“We don’t know what’s going to happen in this situation created by this president,” said one of them, Bella Buitrago, 48. “We’re all extremely nervous.” “We don’t want Mr Maduro… he should leave the country,” said another, Sindry Borges.
Some in Maduro’s administration have broken ranks with him, most prominently his attorney general. Two diplomats resigned this week in dissent: one at the United Nations and another at the embassy in Panama.
The Venezuelan leader has blamed the mounting unrest against him and his policies on the United States, working hand-in-hand with the Venezuelan opposition to wage an “economic war.”