The call to polls described as a "plebiscite" by the opposition, but "illegal" by the government is over Maduro's intention to have a citizens' body elected to redraft the country's basic law.
To detract from the opposition vote, his government was on Sunday holding a dry-run simulation of that election, which is to be held on July 30.
Several Latin American countries and the Catholic Church have criticized the move to draw up a new constitution, while the opposition has slammed it as bid by Maduro to concentrate dictatorial powers to stay in power.
Many voters, wearing white or the colors of the Venezuelan flag, turned up early to the 14,000 makeshift voting tables set up under tents across the country.
"Liberty!" yelled some.
"We are turning out to show our discontent with the government," said 49-year-old Tibisay Mendez.
"We can't find medicines, every day there is less food in the country. And they (Maduro and his officials) only want to hold on to power. We are voting to get them out," she said.
The electoral struggle is being played out against a backdrop of pro- and anti-Maduro demonstrations -- which have left nearly 100 people dead since April 1 and a near-collapse of the oil-rich nation's economy.
Although the National Electoral Council, which sides with Maduro, has not authorized Sunday's vote, the opposition is expecting a big turnout.
Already early Sunday in Caracas there were lines in parts of the city in front of makeshift polling stations.