The amendment, which was passed by the National Assembly by 151 votes to 16, now goes to the upper house of parliament for a final vote.
The approval came after the government removed a number of more controversial clauses, which would have given the authorities greater power to amend the constitution.
After the vote, Prime Minister Nawaz Sharif said: "I congratulate the nation on the passage of the bill which will help create a truly Islamic system.
The introduction of Shariah law, which is based on the Koran and the teachings of the Prophet Mohammed, has been hotly debated since it was proposed after a long campaign by Muslim activists for a return to Islamic values.
It has been fiercely opposed by opposition parties and members of religious minorities on the grounds that it will undermine the fundamental structure of the constitution, and could discriminate against non-Muslims.
Nawaz Sharif insisted the changes will not adversely affect women and minorities in Pakistan.
But lawmakers withdrew a clause that promised the country's minorities that their "personal law, religious freedom, traditions or customs ... and status as citizens" would be protected.
Strong criticism
Members of Pakistan's minority religious groups have strongly condemned the amendment.
Opposition members said it amounts to interference by the state in the religious life of the individual.
They also accused the government of giving supra-constitutional powers to the executives who make new laws.
One clause says the federal government should be under an obligation to prescribe what is right and to forbid what is wrong, as laid down by the Koran and Sunnah, the words and deeds of the holy prophet.
However, the prime minister denied trying to enhance his authority, saying the bill is aimed at making Islam a constitutional cornerstone, and would help fight against crime and corruption.
Our correspondent in Islamabad, Owen Bennett-Jones, says the opposition is stronger in the Senate, and the government may find it difficult to get the two-thirds majority it needs to get the amendment passed.