The vote, which the opposition sees as a power grab by the president, will see the creation of a constituent assembly with the power to rewrite the constitution and override congress.
Security forces used armored vehicles to disperse demonstrators, and gunfire could be heard across the country.
As voting got underway, protestors took to streets in spite of a government ban, and casualties were reported on both sides.
Three people were shot dead in the state of Tichiria – a soldier from the national guard and two teenagers.
In the early hours of Sunday morning, shortly before polls opened, José Felix Pineda, a 39-year-old lawyer standing in the election, was also reportedly shot dead in his home in Bolivar state.
Ricardo Campos, a youth secretary with the opposition Acción Democrática party, was killed during a protest in the north-eastern town of Cumana, according to prosecutors.