Turnout was thin in early voting across the country, in contrast to the long lines for the presidential ballot two months ago, which handed Chavez a third term.
"I'm surprised. In the presidential election I got here at 3 a.m. and there were a lot of people in line. Today I got here at 5 a.m. and I was the first person," said Nathaly Betancourt, who was voting in the western city of Punto Fijo.
The South American OPEC nation appears more focused on Chavez's recovery in Havana from Tuesday's operation, the socialist leader's fourth since he was diagnosed with cancer in his pelvic region in mid-2011.
Government officials on Saturday night said Chavez had regained full consciousness and was giving instructions. His son-in-law, who serves as Science and Technology Minister, acknowledged there had been "moments of tension" during and after the operation, but said Chavez was steadily improving.