The judge cited a possible conflict of interest in the case of Asia Bibi.
Hundreds of riot police had been deployed around the Supreme Court in the capital, Islamabad.
Blasphemy is a highly sensitive issue in Pakistan - critics argue laws are frequently misused to settle personal scores, often targeting minorities.
Last year the Supreme Court suspended Asia Bibi's death sentence and gave her leave to appeal.
A new date for the hearing has yet to be set.
Judge Iqbal Hameed ur Rehman, one of three set to hear the appeal, recused himself from the case on Thursday.
"I was a part of the bench that was hearing the case of Salmaan Taseer, and this case is related to that," he told the court, AFP reports.
Mr Taseer was the liberal governor of Punjab province. He was killed by his own bodyguard in Islamabad in 2011 after speaking out for Asia Bibi.
Family in hiding
Asia Bibi was the first woman to be sentenced to death under Pakistan's blasphemy laws and her case is one of the most controversial.
She was sentenced to hang in 2010 for insulting the Prophet Muhammad during an argument with Muslim women which began over a cup of water. She denies the charge.
Thousands have protested against her and said they would kill her if she were ever released - including the imam in her own village. Her husband and four daughters live in hiding and say they have received many death threats.
Asia Bibi's death sentence had been confirmed by the High Court in Punjab province in October, although no date was set.
Correspondents said the granting of leave to appeal by the Supreme Court was the first glimmer of hope for her family.
Her lawyers say the trial and subsequent appeal in the Punjab high court were flawed.
Pakistan has never executed anyone for blasphemy but some people accused of the offence have been lynched by crowds. Lawyers, judges and those seeking to reform the blasphemy laws have also been threatened, attacked or even killed.
Since the 1990s, scores of Christians have been convicted for desecrating the Koran or for blasphemy.
While most of them have been sentenced to death by the lower courts, many sentences have been overturned due to lack of evidence.
Muslims constitute a majority of those prosecuted, followed by minority Ahmadis.

Baroness Newlove said 15% of victims had been given the opportunity to make a victim statement in 2015/16.
She said there had been little change since 2013 - when figures were first complied - and "more needs to be done".
The Ministry of Justice said it will spend Â£70m helping victims this year.
As part of an official code of practice, every victim who reports a crime is entitled to write a statement about how the offence has affected their life.
If a suspect is convicted in court, a victim statement can be read out before sentencing - as well as later at a parole hearing.
However, in a report about the situation in England and Wales, Baroness Newlove said victims given had been given the chance of making statements in only 15% of cases.
The right of victims to make a statement should be enshrined in law, the commissioner added, with sanctions for police and other agencies if they did not offer the service.
"Enough is enough," said Baroness Newlove, who has campaigned against violence since her husband, Garry, was attacked and killed by youths outside their Warrington home in 2007.
"No-one can claim that victims are 'at the heart of the criminal justice system' when these figures suggest that the Victims' Code is no more than a wish list," she added.
"More needs to be done to support victims of crime."
She added: "There are laws in place to protect the rights of offenders - but nothing to protect the rights of victims. Yet again victims' rights are being ignored."
A Ministry of Justice spokesman welcomed the report, saying it would consider its findings carefully.
The government has allocated Â£67.85m to Police and Crime Commissioners (PCCs) in 2016/17, and again in 2017/18, to support victims of crime, the spokesman said.
"It is vital that blameless victims see swift and certain justice, which is why we have protected the victims' budget and given PCCs almost Â£70m to support victims in their areas.
"We have long committed to strengthening victims' rights, to ensure the most vulnerable get the support they deserve," the spokesman added.
A Pakistani Christian woman on death row for blasphemy has had her appeal adjourned after one of the judges refused to hear the case.
[NEXT_CONCEPT]
All victims of crime should be given the chance to make a statement in court about the impact the offence has had on their lives, the victims' commissioner for England and Wales has said.