Voters strongly opposed government plans for a new constituent assembly with the power to scrap the National Assembly and re-write the constitution.
Venezuela is polarised between backers of President Maduro and the opposition, which wants fresh elections.
A nurse was shot dead while queuing to vote in the capital, Caracas.
Men on motorbikes opened fire, killing 61-year-old Xiomara Soledad Scott, and wounding three others.
The opposition blamed a “paramilitary” gang for the shooting, which prosecutors said they would investigate.
Separately, journalist Luis Olavarrieta was kidnapped, robbed and beaten by what he said was a a group of government supporters, but managed to escape.
More than 100 people have died in clashes and protests in Venezuela since April.
The rector of the Central University of Venezuela, Cecilia García Arocha, said 6,492,381 people voted within the country and another 693,789 at polling stations abroad. However, the vote has no legal status.
The turnout is slightly less than the 7.7m people who voted for opposition candidates at the 2015 parliamentary elections. There are 19.5m registered voters in the country.
Voting yes or no to three questions, 98% rejected the new assembly proposed by President Maduro and backed a call for elections before his term of office ends in 2019.
They also voted for the armed forces to defend the current constitution.