All five attackers were killed.
Save the Children said it has temporarily suspended all Afghan operations after three staff members were killed. Forty-six other employees, who were hiding in a safe room, were rescued.
"We remain fully committed to helping the most deprived children of Afghanistan," Save the Children said in a statement. The global charity, which runs aid programs in 16 of Afghanistan's 34 provinces, reaches almost 1.4 million children in the country.
ISIS claimed responsibility for the attack, which started at 9 a.m. when a suicide bomber detonated a vehicle laden with explosives outside the office gate, according to the media office for Nangarhar province.
Four other assailants stormed the building and were later killed by security forces, said Attaullah Khogyani, a spokesman for the Nangarhar governor.
ISIS' affiliate in Afghanistan claimed responsibility in a statement released by Amaq news agency, the media wing of the terror group.
Images taken as the siege unfolded showed a massive military presence outside the building. Afghanistan's TOLO news channel published footage showing dozens of what it said were Afghan special forces at the scene.
Gunshots were heard ringing out as people appeared to flee.
The wounded were taken to the hospital, Khogyani said.
"Afghanistan is one of the most difficult places in the world to be a child and for humanitarian workers to operate in," said Evan Schuurman, Save the Children's Asia regional media manager, adding that the organization was devastated.
Nicholas Kay, the UK ambassador to Afghanistan, called the attack an outrage and crime against humanity.
"I hope for a quick and safe end to this horrific incident," he said on Twitter.
A loud boom
Ahmad Shah, 29, lives in front of the Save the Children's branch in Jalalabad.
Shah was at home with some guests when they heard a loud boom. All of their windows were damaged, along with the doors. A dozen of them remained huddled inside afterward.
"We don't feel secure as operations are still going on," Shah said.
Shokrullah, who only gave his first name, has a brother who works at Save the Children. He said his brother told him he made it to the safe room with some colleagues.
An uptick in violence has led many organizations to pull out or scale back their footprint in Afghanistan.
The security situation has worsened in the capital of Kabul, where assailants stormed the Intercontinental Hotel on Saturday.
Afghanistan's Interior Ministry said 153 people were rescued from the hotel.
The Taliban claimed responsibility for the hotel attack, but some Afghan officials blamed the Haqqani network, which is aligned with the Taliban but based mainly in Pakistan.
CNN's Ehsan Popalzai reported from Kabul and journalist Ayub Farhat from Jalalabad, while CNN's Joshua Berlinger wrote from Hong Kong.