Opposition officials say one woman was killed and three other people were wounded. They blame the attack outside a church in one of Caracas' poorer districts on pro-government 'paramilitaries.'
An opposition statement says it feels 'great pain' over the shooting.
Turnout was reported heavy for the opposition-sponsored referendum asking voters whether they approve of a July 30 election for a special assembly to draft a new constitution.
Maduro has said changing the constitution is the only way to pull Venezuela out of its deep economic and social crisis.
'I'm calling on the opposition to return to peace, to respect for the constitution, to sit and talk,' he said Sunday. 'Let's start a new round of talks, of dialogue for peace.'
Opposition supporters count votes at a polling station after an unofficial plebiscite against President Nicolas Maduro';s government and his plan to rewrite the constitution, in Caracas, Venezuela July 16, 2017.
But the opposition says the assembly will be rigged in Maduro's favor. It says rewriting the constitution is nothing but a Maduro ploy to turn Venezuela into a socialist dictatorship and destroy dissent.
They hope a strong voter turnout will increase the pressure on Maduro.
One voter who rejects the new constitution summed up the feelings of millions of Venezuelans, telling the Associated Press 'there's no medicine, no food, no security...no separation of powers, no freedom of expression.'
The drop in global energy prices along with government corruption has destroyed Venezuela's oil-rich economy. There are severe shortages of basic goods such as gasoline, flour, sugar, and cooking oil. Supermarket shelves are bare and many Venezuelans cross into neighboring Brazil and Colombia to buy food.
Daily clashes between pro-government marchers, protesters, and police frequently blows up into violence. Nearly 100 people have been killed.
Maduro blames his country's woes on the United States and warns against intervention by the Organization of American States, saying that would surely bring on civil war.