A number of so-called anti-terror laws will give police greater powers of arrest and surveillance - which critics say will turn the country into a police state.
The constitutional amendments are expected to pass.
Mike Hanna, Al Jazeera's correspondent, said the government "has made absolutely clear that it will regard a majority 'yes' vote as an endorsement of its constitutional amendments, regardless of how many people actually vote".
Estimates from the Muslim Brotherhood and the Hesham Mubarak Law Centre, an independent group co-ordinating monitors, also put the turnout around three per cent.
Al Jazeera reporters were outside polling stations all day and saw few people voting, and Reuters described the turn out as a "trickle".
Amnesty International describes the proposed changes as the greatest erosion of human rights in 26 years.
"It is really sad to see Egypt - a republic - turned into a kingdom"
Be Humble, UK
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Human Rights Watch said the amendments "effectively remove basic protections against violations of Egyptians' rights to privacy, individual freedom, security of person and home and due process".
Al Jazeera obtained evidence that suggests the polling system may be badly flawed. And Monday night, the Egyptian Council of Human Rights, a government body, said in a report that there were voting irregularities.
Ayman Mohyeldin, Al Jazeera's correspondent, said he spoke to voters who didn't understand why they were voting and found even ineligible voters were able to take part.
Mohyeldin also said government employees were taken en masse by buses to polling stations.
Amal Oweid, an Egyptian he spoke with, said: "I am here to vote for Hosni Mubarak ... I am here to vote for him as president."
She did not know how to read or write and did not know what was on the ballot.
Oweid said: "A guy came with me and he said mark here and I marked on the green circle ... I didn't know what the ballot said."
Mohyeldin reported that he was able to cast a ballot without providing appropriate Egyptian identification.
He said: "I came to the polling station [and] presented a press ID issued by the ministry of information that clearly stated that I am an American citizen working for Al Jazeera."
"The supervisor asked me whether I was born in Egypt. I replied yes and I told him my father was Egyptian. I was handed a ballot and allowed to vote. At no time did I mislead authorities about my nationality or my identity."
There is no guarantee that the ballot will be tallied but the instance highlights major loopholes in the voting system, Mohyeldin said.
The amendments, passed by parliament a week ago after a secretive drafting process controlled by the ruling National Democratic Party (NDP), target mainly the Muslim Brotherhood, a group which has built up strong support in Egyptian society since it was founded in 1928.
|Gamal Mubarak, head of the ruling party, says|
he has no presidential ambitions [Reuters]
Under the amended constitution, Mubarak and the ruling party could dissolve the existing parliament and hold new elections under a new voting system which would make it more difficult for the Brotherhood to win seats.
Brotherhood leaders say the government's aim is to push out the opposition and make it easier to install Mubarak's son, Gamal, as the country's next president.
Gamal Mubarak, head of the NDP, denies he has presidential ambitions. In a briefing on Sunday, he said there was no link between the amendments and any plan to dissolve parliament.