A group of gunmen on motorcycles attacked Venezuelan voters who were lined up at an opposition polling site in the traditionally pro-government neighborhood of western Caracas on Sunday.
A 61-year-old woman was killed and four others were wounded in the shooting. Video posted on social media showed hundreds of people running as the pro-government group drove past firing into the crowd.
Sunday's unofficial, opposition-led referendum was held to show a symbolic rejection of President Nicolas Maduro's plan to rewrite the constitution. Several Latin American countries, as well as the Catholic Church, have criticized Maduro's plan to re-write the country's constitution, the Agence France-Presse reports.
About an hour after the shooting Maduro issued a statement on state television and failed to mention the incident. Instead, he blamed the violence on the opposition.
"I'm calling on the opposition to return to peace, to respect for the constitution, to sit and talk," Maduro said. "Let's start a new round of talks, of dialogue for peace."
Maduro, who many suspect wants to re-write the constitution to retain his power, has argued that a new constitution would help bring Venezuela out of its economic and political crisis, while also deterring any "coup-plotters."
Democratic Unity, a coalition of some 20 opposition parties, has printed millions of ballots, hoping voters will turn out to put more pressure on the current government.
Polls currently show that only about 20 percent of Venezuelans are in favor of rewriting the late Hugo Chavez's 1999 constitution.
The Associated Press contributed to this report.