Reports of violence mar campaign for widely supported charter that would limit powers of President Robert Mugabe.
Around six million eligible voters began casting their ballots on Saturday at 05:00 GMT at 9,456 polling stations dotted across the southern African country. Polls across Zimbabwe are due to close at 17:00 GMT.
Official results are expected to be released within five days of the vote.
The country’s main political parties, including Mugabe’s ZANU-PF, are in favour of the proposed law changes, making the simple majority needed for a “yes” vote a near certainty.
Al Jazeera’s Haru Mutasa, reporting from the capital, Harare, said “many people are hoping for a change, mainly an economic one … People want jobs, because right now people are struggling”.
An attack on activists and officials of Prime Minister Morgan Tsvangirai’s party on the eve of the vote marred what had been a blood-free campaign.
Although authorities have targeted pro-democracy groups in the runup to the vote, arresting their leaders and seizing equipment, few deaths have been reported.
During the attack on Friday, members of Tsvangirai’s Movement for Democratic Change (MDC) were punched as they put up posters urging voters to approve the proposed law.
The MDC suggested the attack was perpetrated by supporters of Mugabe’s Zimbabwe African National Union-Patriotic Front.
Police dismissed the incident as stage-managed by a BBC television crew, who were also attacked, to “portray Zimbabwe as a violent country”.
The new constitution would curb the presidential powers that Mugabe has enjoyed during his 33-year rule and lay the groundwork for elections due in July that would end an often acrimonious power-sharing deal between Mugabe and
“This constitution is fairly straightforward, the election is what is uncertain … The problem with Zimbabwe has always been that too much power has been in the hands of the president,” our correspondent said.
Although the draft has the backing of both 89-year-old Mugabe and his rival Tsvangirai, 61, tensions between supporters of the two main parties are seething after a series of bloody elections in the crisis-weary country.
“The attacks are a clear testimony that ZANU-PF wants to embark on acts of violence,” said MDC spokesman Douglas Mwonzora.
During 2008 elections more than 180 people were killed and 9,000 injured, according to Amnesty International, sparking a national crisis that forced Mugabe into his power-sharing deal with Tsvangirai.
Many see the government’s harassment of activists ahead of the referendum as a prelude to a more serious election crackdown.