Maduro says rewriting the constitution will promote peace, but the opposition feels it's a move to install a dictatorship.
"They are speaking with their hearts that they support democracy," said Juan Fernandez, who voted in South Florida.
There were seven voting sites open in Broward and Miami-Dade counties.
"So far today, up until this point, 7,000 people have voted here," said Devorah Sasha, an organizers at a voting site serving the North Miami Beach and Avenutra area.
At the Watsco Center in Coral Gables hundreds showed up early to cast their ballots.
"There is no problem with the constitution that we have," Hirem Rodriguez, who voted in Coral Gables, said. "The problem is with the government that we have."
Venezuelans from all over the world, from Spain and Germany to South Korea and Saudi Arabia,also took part in the vote.
Although the vote has no legal impact, South Florida representatives said the referendum is important because it will send a message to the Venezuelan government.
"It is incredible, the enthusiasm, the passion, Venezuelan-Americans (have) for democracy to reject the dictatorial reaches of Maduro and they're saying yes to the National Assembly," U.S. Rep. (R. Fla) Ileana Ros-Lehtinen, said.
U.S. Rep. Mario Diaz-Balart (R. Fla.) agreed.
"It's important that we stay united and helping the opposition and rejecting this dictatorships desired stay in power," he said.
The success of the symbolic referendum will be measured by how many millions participate.
The Democratic Unity opposition coalition, who printed 14 million ballots for voters inside and outside the country of 31 million people, expect turnout a high turnout, and analysts say participation by more than 8 million people would significantly hike pressure on the government two weeks before it holds elections for a constitutional assembly.
Polls show the socialist government would likely lose a presidential election under the current constitution, and it says it wants a rewrite that would advance its revolutionary system.