Pakistan`s prison guidelines require that a prisoner stand on the gallows.
Rights groups have said that hanging a handicapped person would constitute cruel and degrading treatment.
Abdul Basit, 43, is paralysed from the waist down and uses a wheelchair after becoming ill in prison.
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Pakistan reintroduced the death penalty in December 2014 and has hanged 239 people since.
At the time, the government said it was a measure to combat terrorism after the Taliban massacred more than 150 people, most of them children, in a Peshawar school.
The condemned man was convicted six years ago of murder and was to have been hanged in Lahore last month - but that was postponed.
A court then ordered the jail authorities to go ahead with the hanging, even though his mercy petition filed on 22 July before the president is still pending. It is unclear if any time limit was imposed on the most recent postponement.
Campaigners say that prison guidelines do not cover the hanging of a paralysed person.
"The jail manual only provides for hanging as a method of execution, and lays down methods to calculate the right length of rope to ensure that hanging does not lead to protracted strangulation," Wassam Waheed, a spokesman for Justice Project Pakistan (JPP) told the BBC.
"The rules presume that the convict [can] walk up to the gallows, which is not possible in Abdul Basit`s case."
A trial court issued a death warrant against Abdul Basit on Friday and ordered jail authorities to hang him on 22 September.
Both the Supreme Court and the Lahore High Court have given their consent to the execution.
Rights groups say that there is a danger that the hanging could go wrong and end up being a breach of the prisoner`s dignity - which is protected by Pakistani laws.
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