Shahbaz Bhatti, a Christian, was shot by gunmen who forced their way into his car in the capital Islamabad. He was rushed to Shifa Hospital after the attack but was pronounced dead on arrival.
Although no group has come forward to claim responsibility, there are reports that pamphlets issued by al-Qaeda and the Taliban were found at the site of the attack.
Mr Bhatti had long campaigned for reform of Pakistan's blasphemy laws, which makes insulting Islam a crime punishable by death.
His murder comes two months after the Governor of Punjab, Salmaan Taseer, was assassinated by his own bodyguard over his support for changes to the blasphemy laws, which rights groups say are being misused to persecute Christians.
Release International said it was "absolutely devastated" by news of Mr Bhatti's death.
"It is massively unfair for the majority of Pakistanis who want to live in peace that a handful of groups are insistent on assassinating anyone who doesn't share their view," it said.
"This is a massive loss for the people of Pakistan.
"Our prayers are with his family."
Release said the murders of Taseer and Bhatti had left campaigners and other politicians who have spoken up for minority rights fearing for their lives.
They include Sherry Rehman, who was forced to back down on her Bill to reform the blasphemy laws after coming under intense pressure from extremists.
Release said the EU, UK and US must intervene to make sure that the President and Prime Minister of Pakistan launch a constitutional review and move to reform the blasphemy laws.
It questioned whether the likes of Britain and other EU countries should continue to send millions of dollars in aid to Pakistan while people continue to be killed because of their views on religion or the blasphemy laws.
"There are certain elements that are intent on trying to get rid of any voices that speak up for minorities and seek change for Pakistan," it said.
"This killing has made constitutional reform more urgent now.
"This is the moment for change in Pakistan because it cannot allow extremists to dominate the agenda."
Release called upon Pakistan to ensure that the perpetrators were held to account.
"The President and Prime Minister cannot let his death go undealt with. The perpetrators must not be treated as martyrs. They should be shamed," it said.
Mr Bhatti's murder has also been condemned by the Centre for Legal Aid, Assistance and Settlement, a charity providing free legal support to persecuted Christians in Pakistan.
CLAAS' UK Coordinator Nasir Saeed said the minister's death was a "terrible blow" for Pakistani Christians and that there was uncertainty over their future.
"Shahbaz Bhatti was one of the few people in parliament who dared to speak up for Christians and now that he is gone, we have no voice," said Mr Saeed.
"Everyone who spoke up for Christians has been silenced by the extremists and we cannot say anything anymore.
"At this point in time, it is not clear what avenues are left open to us. The EU, the Pope, the Archbishop of Canterbury, the UN, have all raised their concerns and yet the government in Pakistan continues to do nothing.
"It has bowed down to the will of religious groups and so long as that is the case, more innocent people are going to die."
Mr Saeed appealed to the church in the UK to pray for Christians in Pakistan and for the government to change the blasphemy laws.
He added that CLAAS would be contacting the Pakistani High Commissioner and the Foreign Office to urge their intervention on behalf of Pakistan's minorities.
