The 51-year-old Christian woman has been on the death row since November 2010 after she was convicted on charges of committing blasphemy during an argument with two Muslim women in Sheikhupura.
The top judge added that the expression "proof beyond reasonable doubt" was of fundamental importance to the criminal justice and was one of the principles which sought to ensure that no innocent person was convicted. The incident led to allegations that she had blasphemed the Prophet Muhammad. Salman Taseer, the governor of Punjab province, was shot and killed by one of his guards in 2011 for defending Bibi and criticizing the misuse of the blasphemy law.
A journalist who visited her in prison before the verdict said she appeared to have memory loss and confusion.
The alleged incident occurred when Bibi took a sip of water while she was working.
Chief Justice Saqib Nisar read out the ruling saying she was free to go, if not wanted in connection with any other case.
Shortly after the ruling, hundreds blocked a key road linking Rawalpindi with Islamabad.
Sources in the administration told Dawn that Rangers and Frontier Constabulary had been called as part of measures to step up security in Islamabad. Similar rallies are being held elsewhere as police urge demonstrators to disperse peacefully.
"Finally Asia Bibi has won", her lawyer, Saiful Malook, told The Times.
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But federal authorities say the bombs Sayoc allegedly sent were real and a danger to their recipients. Investigators believe that Sayoc made the pipe bombs in the van, two law enforcement sources said.
Aasia Bibi was accused of insulting Prophet Mohammad, an allegation that can incite violence in conservative Pakistan.
The leader of the Tehreek-e-Labaik (TLP) party also called for the ouster of Prime Minister Imran Khan's government over the case of Asia Bibi, who was acquitted by a Supreme Court panel earlier in the day.
The Supreme Court has banned local media from reporting on the case until the judgement is announced.
She appealed to the Lahore High Court, which upheld the decision in October 2014, with Ms Bibi denying all charges and taking the case to the Supreme Court.
Bibi was condemned for allegedly making derogatory remarks about Islam after neighbours objected to her drinking water from their glass because she was not Muslim. They asked her to convert to Islam, which Asia refused.
Critics of Pakistan's blasphemy laws have long claimed that they are open to abuse, and often used by accusers simply to settle petty scores or oppress religious minorities. His assassin, Mumtaz Qadri, was executed in 2016 and has been feted as a hero by hardliners, with a shrine to him built by Islamists just outside the capital.
Islam is Pakistan's national religion and underpins its legal system.