International observers said the turnout appeared lower than during parliamentary polls last December.
"Rain played a role but it is not the only factor" affecting voter turnout, said Johan Van Hecke, the head of the European Union observer mission.
The voting took place "in general in a calm and orderly way" he said, adding that "not a single incident or complaint was reported".
The electoral commission also said turnout had been low, blaming it on tensions following Vieira's killing, but gave no figures.
Vieira was shot dead by soldiers in March in apparent revenge for the killing of the head of the army.
One leading contender was also killed during the election campaign.
Test for region
The vote is a test not only for the country but for a region worried at the retreat of democracy after coups in Guinea and Mauritania and a deepening political crisis in Niger.
"The real test for Guinea-Bissau is not whether the election is held peacefully, but whether state institutions have the capacity to prevent the country from sliding into chaos in the aftermath," said Kissy Agyeman-Togobo of IHS Global Insight.
"The military has been far too dominant … so there is a real need for the international community to offer support for capacity building."
The three frontrunners have all pledged peace and justice.
Malam Bacai Sanha, of the ruling party, was interim president from 1999 to 2000 after a coup and brief civil war.
Kumba Yala, who was overthrown as president in a 2003 coup, is a former philosophy professor who has the backing of the biggest tribe, the Balante.
Henrique Rosa, standing as an independent, served as interim president between the overthrow of Yala and the 2005 election won by Vieira.
If no candidate wins an overall majority in the first round, the election will go to a run-off between the two highest-placed contenders on July 28.