Fidesz has two-thirds of the seats in parliament, but the measures were approved overwhelmingly as opposition MPs boycotted the vote.
The amendment tightens up the laws on higher education, homelessness, election campaigns and family rights.
It defies constitutional court rulings.
The EU and US had urged Fidesz to respect democratic checks and balances.
In response, Prime Minister Viktor Orban accused the EU of interfering in Budapest’s domestic affairs.
The lengthy amendment overturns earlier constitutional court rulings and limits the court’s right to challenge laws passed by parliament in future. It also includes:
It is the fourth amendment to Hungary’s new constitution since it came into force just 14 months ago – a fact which helps underpin criticism that the new constitution was both hurried and flawed.
Critics at home and abroad say the amendment dismantles the architecture of democracy established since the fall of communism, and allows Fidesz to cement its own ideology at the heart of the state.
Several thousand people protested in Budapest on Saturday against the proposed changes.
Fidesz argues the changes are necessary to make a clean break with the previous constitution, which was adopted in 1989 when Hungary threw off communist rule.
But Viktor Orban is under pressure at least to postpone Monday’s vote until experts from the Council of Europe – Europe’s main human rights watchdog – can examine the amendment.
German MEP Alexander Lambsdorff urged the European Commission to investigate a possible “systematic violation of European values” by the Hungarian government ahead of the vote, the newspaper Der Tagesspiegel reports.
In a separate development, Viktor Orban described as “scandalous” a court decision against the government over state-imposed gas price cuts.
He said he would not accept the ruling scrapping recent 10% price cuts and would instead submit a new proposal to lower prices even further.
The government’s measure is popular with many Hungarians who are struggling to pay their bills, but energy companies have complained that they have to foot the bill.
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