The allegations against Bibi date back to June 2009, when she was labouring in a field and a row broke out with some Muslim women who alleged that she committed blasphemy against Prophet Muhammad (Peace Be Upon Him).
Later, two women refused to drink from the container she had touched because she was not Muslim.
Islamists have demanded her execution.
Ms Bibi, a mother of five, has been offered asylum by several countries and will most likely leave the country if released over worries about her safety. In 2011 Punjab province governor Salman Taseer was shot and killed by one of his guards for defending Ms Bibi and criticising the misuse of the blasphemy law.
Bibi's case has been extremely divisive in Pakistan.
Blasphemy against Islam and its Prophet is a sensitive subject in Pakistan, where the crime can carry a compulsory death sentence. At least 1,472 people were charged under Pakistan's blasphemy laws between 1987 and 2016, according to statistics collected by the Center for Social Justice, a Lahore-based group. The Pakistani Supreme Court today set aside that conviction.
"Should the court verdict be lenient against Asia Bibi, they warned of countrywide chakka jaam - laying siege to traffic, a form of protests in South Asia where protesters stop, attack and burn vehicles". The two Muslim women who pressed charges against Bibi denied they quarrelled with her, saying her outbursts against Islam were unprovoked.More news: LeBron hails Ball, Stephenson after Lakers win again
The group's emir for the Khyber Pakhtunkhwa province said: "The objective of this protest is to raise awareness that if any such judgment is delivered in this sensitive case that grants concessions to the blasphemer Asia, then we will protest all over the country".
Her daughter, Eisham Ashiq, had previously told the AFP news agency that if she were released: "I will hug her and will cry meeting her and will thank God that he has got her released".
Aasia Bibi, whose case has become iconic of fair-trial concerns in such accusations, was freed in a move the far-right Tehreek-e-Labbaik Pakistan (TLP) party has said it will respond to with countrywide protests.
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.
"The patron in chief of TLP, Muhammad Afzal Qadri, has issued the edict that says the chief justice and all those who ordered the release of Asia deserve death", said party spokesman Ejaz Ashrafi.
"We urge the government of Pakistan to provide necessary security to Asia and give her a safe passage to a place of peace and security. We hope this time she will be completely exonerated and this wrongful conviction will finally be overturned as this is her last chance to be heard at court".