Reports from across the country indicated low voter turnout.
The UN Security Council has said it deeply regrets Zimbabwe's decision to go ahead with the presidential poll.
It said conditions for a free and fair election did not exist, but stopped short of saying it was illegitimate.
President Robert Mugabe is assured of victory after opposition candidate Morgan Tsvangirai boycotted the poll. Vote counting has started.
A top African Union diplomat said African leaders could find a credible solution to Zimbabwe's problems.
AU commission chairman Jean Ping emphasized that democracy and human rights were shared values of all the AU countries.
"We are here playing the role of guardian of these values, so when we see there has been violations of some of these shared values, it is our duty to react and call some of our members to order," he said.
Mr Ping was speaking in Egypt ahead of next week's AU summit.
Mr Mugabe is expected to attend the summit and the BBC's Peter Biles in Johannesburg says he will want to declare victory before leaving.
The European Union and the US earlier dismissed the vote as meaningless.
Foreign ministers for the Group of Eight nations (G8) meeting in Japan said they could not accept the legitimacy of a government "that does not reflect the will of the Zimbabwean people".
US Secretary of State Condoleezza Rice said they would consult other members of the UN Security Council to see what "next steps" might need to be taken.
"There was a strong sentiment... that what is going on in Zimbabwe is simply unacceptable in the 21st century and it can't be ignored by the international community," she said.
The US ambassador to the UN, Zalmay Khalilzad, read out a statement by the Security Council which said members "agreed that conditions for free and fair elections did not exist and it was a matter of deep regret that the election went ahead in these circumstances."
The statement, backed by all 15 council members including South Africa, China and Russia, stopped short of declaring the election illegitimate because of South African opposition.
People will not feel safe moving about with an unmarked finger - Zimbabwean citizen.Harare cowed for one-man pollElection: At a glanceIn pictures: Mugabe election
Mr Khalilzad added that the council would return to the issue in the coming days:
"We have already started discussions with some colleagues on a resolution that would impose appropriately focused sanctions on the regime, assuming conditions continue as they have during the last period," he said.
However, diplomats said that because of resistance from South Africa, China and Russia, any sanctions were unlikely to be imposed by the council.
At a news conference held in Harare before polls closed, Zimbabwean opposition leader Morgan Tsvangirai described the election as "an exercise in mass intimidation".
Mr Tsvangirai, who boycotted the poll because of violence, said people across Zimbabwe had been forced to take part and urged the international community to reject the vote.
Zimbabweans explain why they are voting in the election"Anyone who recognises the result of this election is denying the will of the Zimbabwean people," he said.
The MDC leader has been taking refuge at the Dutch embassy for most of the past six days.
The Zimbabwe Election Support Network, a monitoring group, reported that people had been forced to vote in most rural areas.
Fear of retribution
A Zimbabwean journalist said militias loyal to Mr Mugabe had gone door-to-door in townships outside the capital, Harare, to coerce people.
Despite the pressure, Marwick Khumalo, who heads of the Pan-African parliamentary observer mission, told the BBC that overall turnout had been low and the mood sombre.
But the state-owned Herald newspaper said there had been a huge voter turn-out in the election.
Justice Minister Patrick Chinamasa said that people were aiming to preserve Zimbabwe's independence.
African voices on Zimbabwe's poll crisisIn pictures
Mr Mugabe came second to Mr Tsvangirai in the first round of the presidential vote in March.
Since then, the MDC says some 86 of its supporters have been killed and 200,000 forced from their homes by militias loyal to Zanu-PF.
The government blames the MDC for the violence, but Mr Mugabe has suggested negotiations with the MDC were possible - "should we emerge victorious, which I believe we will".
Mr Tsvangirai has said negotiations would not be possible if Mr Mugabe went ahead with the run-off.
BBC NEWS REPORT.
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