Shoaib Sarwar, who was convicted in 1998, was set to be hanged in Rawalpindi's Adiyala jail on Thursday following orders issued by another court last week, despite outrage among rights groups.
Pakistan has had a de facto moratorium on civilian hangings since 2008. Only one person has been executed since then, a soldier convicted by a court martial and hanged in November 2012.
"We are relieved to have managed to avert this impending injustice through a stay order," said Maryam Haq, a lawyer from the non-profit group Justice Project Pakistan.
Haq said her organisation had argued that the execution should be stayed on the basis that Sarwar had been in prison for over 18 years -- longer than a life sentence -- therefore execution would mean he was being punished twice for the same crime.
They also argued that since Sarwar was a complainant in a petition for the abolition of the death penalty currently being heard by the Supreme Court, that case should be decided upon first.
"Shoaib's execution would be an unimaginable violation of his constitutional rights and we will continue to fight until this black warrant has been dismissed," she said.
"Pakistan should immediately scrap apparent plans to carry out the first civilian execution in almost six years and instead impose a moratorium on the use of the death penalty as a first step towards abolition," the group said in a statement.
Sarwar is currently being held in a jail in the northwestern town of Haripur, some 25 kilometres (16 miles) from Islamabad.
In June last year the newly elected government of Prime Minister Nawaz Sharif scrapped the moratorium in a bid to crack down on criminals and Islamist militants.
All execution orders in Pakistan must be signed by the president.