There are 545 seats up for grabs and those elected would essentially replace the current National Assembly -- which is controlled by opponents of President Nicolás Maduro's government.
The newly elected body would rewrite the 1999 constitution, the cornerstone of former President Hugo Chavez's "Bolivarian Revolution," which extended presidential term limits and allowed for indefinite re-elections.
The vote will be split into two categories -- some voters will register by municipality, others based on the industry in which they are employed.
Opponents slam vote
Representatives of Venezuela's opposition and leaders abroad have spoken out against the vote, saying it will erase the last remaining vestiges of democracy in the crisis-ridden country.
A two-day general strike was organized by the opposition in defiance of the vote. Businesses throughout Caracas were shuttered on the first day of the strike Wednesday, as barricades blocked the streets.
Maduro critics also held an unofficial vote on July 16 to demonstrate public opposition. More than 7 million Venezuelans -- nearly 40% of the voting population -- cast ballots against Maduro's proposals
in the non-binding referendum. They also announced a boycott of Sunday's vote and said they would refuse to recognize its results.
US President Donald Trump criticized the vote, saying the White House would take "strong and swift economic actions" against "a bad leader."
Also on Wednesday, the US Treasury Department imposed sanctions on at least 13 current or former leaders in Maduro's government
who were suspected of violating human rights.
Tension got red hot starting in 2015
Opposition leaders won a majority of seats in Venezuela's National Assembly in midterm elections in December 2015.
It seemed like a potential turning point -- the National Assembly could vote to impeach Maduro, who had verbally clashed with opposition leaders since becoming president in 2013.
But before they were sworn into office, Maduro stacked the Supreme Court with his supporters to block any impeachment attempts. Political gridlock and tension brewed.
Things got worse in March
The Maduro-backed Supreme Court briefly attempted to dissolve the National Assembly, sparking a wave of nearly daily protests that have continued since March.
More than 100 people have been killed during the protests, including one person who died Wednesday in the western city of Merida.
The crisis sparked massive migration out of the country to neighboring Colombia and Brazil and other countries -- including Canada and Spain.
Maduro: Vote is 'democratic'
Despite the fierce criticism surrounding Sunday's vote, Maduro claims the Constituent Assembly is democratic and that there was no need to hold a constitutional referendum, as Chavez did in 1999.
Maduro said the role of the new body will be to "perfect" the current constitution and promises that the changes will help the oil-rich nation climb out of its crippling economic crisis.
"We need order and peace, we need our country to reconnect to its identity. There is only one option and that is the Constituent Assembly," Maduro said.
In addition to the strike, the opposition has vowed to continue to stage protests, including a massive march scheduled to take place in Caracas on Friday.