The amendment, proposed by President Hosni Mubarak, will allow multi-candidate presidential elections for the first time in Egypt.
The 454-seat house, dominated by Mubarak's ruling National Democratic Party (NDP), approved the amendment by a show of hands on Tuesday.
Aljazeera learned that 405 of the total 454 members of parliament voted in favour of the amendment.
Opposition parties and groups aligned with the banned Muslim Brotherhood walked out of the parliamentary session in protest, saying the amendment was inadequate.
Egyptian opposition Kifaya (enough is enough) Movement criticised the so called reforms.
In a statement released on Wednesday, the movement said that the ruling party passed impossible conditions with regard to amending article 76 of the constitution, preventing people from the right to vote.
Earlier Kifaya refused what it described as "piece by piece reform", announced its decision to boycott the presidential elections and called on boycotting the referendum on amending the article.
Egypt's parliament is dominated
by Mubarak loyalists
On Tuesday, the movement also called for the launch of a political agitation and urged the Egyptian people to boycott the referendum on the constitutional amendment.
The leader of the opposition alliance, Khalid Muhyi al-Din, said he had withdrawn himself as a presidential candidate.
In a related development, the leader of the opposition Nasserite Party suspended party MP Haydar Baghadadi for supporting the controversial amendment in violation of the party line.
Mubarak, 77, agreed in February to amend the constitution to allow rival candidates to stand, although he has yet to announce whether he will run for a fifth six-year term in the presidential election in September.
However, critics have said the proposed reforms will be ineffectual as election candidates will still require approval from the NDP.
Egypt's Shura Council, or upper house of parliament, passed the amendment on Sunday despite all opposition parties voting against it.
Critics want Mubarak to step
down after four six-year terms
The opposition says the text contains conditions that will make it almost impossible for opposition political groups to nominate candidates, and effectively shuts out independents.
The Egyptian People's Council will discuss the final draft of article 76 of the constitution, allowing the nomination of more than one candidate in the presidential elections.
Approving the amendment requires the approval of at least two-thirds of the council members, before conducting a public referendum at the end of May.
In the meantime, the Egyptian opposition has heightened pressure on the government, calling for additional measures to guarantee honesty and fairness of the elections.
Opposition parties and independent sides have expressed their reservations over the amendment.
Prior to the adoption of the bill, Hussein Abd al-Ghani, Aljazeera's Cairo news bureau chief, interviewed Muhammad Mursi, a member of the Egyptian parliament and the head of an alliance of independent MPs aligned with the Muslim Brotherhood.
"The whole amendment contradicts articles 8 and 40 of the Egyptian constitution: equality of opportunities and equality of citizens' rights and duties vis-a-vis the constitution," Mursi said.
"The whole amendment contradicts articles 8 and 40 of the Egyptian constitution; equality of opportunities and equality of citizens' rights and duties in front of the constitution"
Muhammad Mursi, MP and head of alliance of independent MPs aligned with Muslim Brotherhood
According to him, there are three main reservations about the amendment:
For one, it is impossible to carry out the voting process in one single day. All citizens will not be given a fair chance to cast their ballots.
Next, the supposed guarantees regarding the seriousness of nomination, are no guarantees. In fact, they will prevent the nomination of those the ruling party and the government do not approve of.
"We reject the current text of the article. We have presented a clear proposal to the legislative committee, but it has not been considered."
Finally, with regard to the committee overseeing elections, Mursi said:
Mursi said: "We will reject this article and it should be amended."
In yet another protest, more than 4000 members of the Muslim Brotherhood demonstrated on Monday in front of a mosque in Asyut governorate, Aljazeera's Cairo correspondent reported.
They were protesting against the arrest of 26 Asyut University students and 10 teachers - all members of the Brotherhood.
The protesters called for the release of the detained people and pledged to stick to their demand for political reforms.