Speaking on condition of anonymity, an official at the Interior Ministry said the ban was overturned as a result of enormous pressure from the United States and Britain.
"They threw an outright threat of suspending our aid," said the official.
The charity's offices across Pakistan would be allowed to re-open from Monday, the official said.
Police locked the gate of Save the Children's office in the capital Islamabad on Thursday and posted a notice saying the building was sealed.
Authorities gave the aid group's staff 15 days to leave Pakistan.
On Friday, Interior Minister Chaudhry Nisar Ali Khan said the charity was banned because it was involved in "anti-Pakistan" activities. He didn't elaborate.
Officials have blamed the NGO for hiring the doctor who was later said to have helped the American CIA track down al Qaeda chief Osama bin Laden in the northern city of Abbottabad.
Save the Children denied any link with doctor Shakil Afridi or the CIA.
The charity has agreed to call back some of its foreign staff members about whom Pakistani intelligence agencies have raised objections, the official added.