Xiomara Escot, 61, was killed when a pro-government armed group opened fire at the El Carmen Church polling station in Catia, an impoverished neighbourhood in Venezuela's capital, Caracas.
More than seven million voters took part in the opposition-organised referendum on Sunday, according to academics monitoring the poll.
Voters strongly opposed President Nicolas Maduro's plan for a new constituent assembly with the power to scrap the National Assembly and rewrite the constitution.
The chief prosecutor's office confirmed Escot - who was a nurse - had been killed and four others wounded in the incident.
Video posted to social media showed huge crowds outside the church before running in panic as men on motorbikes zoomed past and shots rang out.
Mr Maduro made no mention of the incident in comments on state television shortly after the official close of opposition polls but called for an end to violence that he blamed on the opposition.
He said: "I'm calling on the opposition to return to peace, to respect for the constitution, to sit and talk.
"Let's start a new round of talks, of dialogue for peace."
The opposition however has blamed a "paramilitary" gang for the shooting, which prosecutors said they would investigate.
Across Venezuela, voters overwhelmingly backed proposals to halt Mr Maduro's plans.
Voting on three questions, 98 per cent rejected the new assembly proposed by President Maduro and backed a call for elections before 2019.
They also voted for the armed forces to defend the current constitution.
The rector of the Central University of Venezuela, Cecilia GarcÃa Arocha, said 6,492,381 people voted inside Venezuela and another 693,789 at polling stations abroad. However the vote, dismissed by Mr Maduro as illegal, was largely boycotted by government supporters.
