At least 12 people were injured in the assault, which started when a suicide bomber detonated explosives at the gate, according to Hataullah Khogyani, a spokesman for Nangarhar province.
At least one assailant then stormed the building and was later killed by security forces, Khogyani said. Offices were searching the third floor of building to make sure it was safe, he added.
It's unclear who is responsible for the attack. A spokesman for the Taliban, Zabiullah Mojahid, denied responsibility for the attack in a statement sent to members of the media.
Images from the scene showed a massive military presence. Afghanistan's TOLO news channel published footage showing dozens of what it said were Afghan Special Forces members at the scene.
Gunshots were heard ringing out as people appear to flee.
The wounded were taken to the hospital, said Khogyani.
Evan Schuurman, Save the Children's Asia regional media manager, said the aid agency was devastated by the news. It is not known if any Save the Children staff were inside or close to the building at the time of the attack.
"Our primary concern is for the safety and security of our staff. We are awaiting further information from our team and cannot further at this time," said Schuurman.
Save the Children is a non-governmental organization that carries out humanitarian work and advocates for young people across the globe.
Nick 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 their glass windows were damaged, along with the doors. After that, a dozen of them remained huddled inside.
"We don't feel secure as operations are still going on," Shah said.
Shokrullah, who only gave CNN his first name, has a brother who works at Save the Children. He said his brother had told him he made it to a safe room in the building with some colleagues.
An uptick in violence has led many organizations to pull out or scale back their footprint in Afghanistan.
The International Committee of the Red Cross (ICRC)
announced in October it would reduce its presence in Afghanistan after its staff were directly targeted multiple times, with at least six Red Cross aid workers were killed
in February.
The security situation has worsened in the capital of Kabul, where just days ago assailants stormed the Intercontinental Hotel.
At least 22 people -- 14 of whom were foreign nationals -- were killed during an hours-long standoff at the hotel, which sits on the edge of town behind checkpoints on a hill.
Afghanistan's Interior Ministry said 153 people were rescued from the hotel.
A reporter for Afghanistan's TOLO news channel, who survived by hiding on a balcony
, described to CNN horrific scenes of attackers searching for victims room by room and desperate guests jumping from balconies.
The Taliban released a statement claiming responsibility for the hotel attack. But some Afghan officials blamed the Haqqani network, which is aligned to the Taliban but based principally in Pakistan.
