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. Votes are now being counted.
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 for Egypt.
In the latest condemnation of the poll, UK Prime Minister Gordon Brown called it "a new low".
"The world is uniting in rejecting the illegitimate regime of Robert Mugabe," he said in a statement.
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".
Morgan Tsvangirai on the day of polling
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.
Earlier, the Security Council issued a statement 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."
But 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
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.