Government employees were bussed to polling stations, but some booths saw only a trickle of people come through.
Authorities had billed the referendum as a key test of support for tentative reforms.
“I can’t say that more than three to five percent turned up today,” confessed one embarrassed officer at a polling station in Cairo’s Khedive secondary school.
Another official at a separate booth tried to hide an electoral register that showed most names not ticked off, according to news agency AFP.
“Maybe we got 30 percent or more,” a government employee at Ahmed Lufti primary school said. But thick stacks of unused ballot papers piled up on his desk told a different story.
Policemen deployed to protect polling stations intervened to ask journalists to leave.
Authorities had been seeking endorsement of the controversial reform, which has been slammed as a sham.
Opposition parties, including the banned Muslim Brotherhood, had called for a boycott of the vote.
Some activists who staged protests against the referendum were set upon by supporters of the governing party.
The opposition says the proposed changes include restrictions that ensure the ruling party would retain power.
But the government of Hosni Mubarak said the amendment’s conditions are needed to guarantee that only serious candidates would run.
President Mubarak, 77, is seeking a fifth six-year term in office in September polls.
Despite a campaign for a “Yes” vote, with large banners erected in Cairo carrying slogans such as “Yes to Mubarak, yes to freedom”, many voters interviewed by AFP were unclear over what exactly they were voting for, thinking they were voting to re-elect Mr Mubarak.
Polling officials acknowledged that such misunderstandings were widespread among voters how had been used to single-candidate elections for the presidency.
“Many people thought they had to vote for the presidency and we had to tell them it was for the amendment,” one officer said.