At least one suicide bomber blew himself up at the gate of the compound, opening the way for gunmen to enter the office.
Residents on social media posted images of those fleeing the offices, including children.
"The there was a blast and the target was Save the Children", Khogyani said, as cited by Reuters. Afghanistan's TOLO news channel published footage showing dozens of what it said were Afghan Special Forces members at the scene.
Meanwhile, an official on condition of anonymity said the suicide vehicle bombing occurred next to the office of non-governmental organisation Save the Children and a gun battle is going.
Mohammad Amin, who was inside the compound when the attackers stormed inside, told AFP from his hospital bed that he heard "a big blast".
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He said that so far two attackers have been killed.
However, the Taliban was quick to distance itself from Wednesday's attack and said they were not involved.
Save the Children carries out education, healthcare and protection work for Children in Afghanistan.
There are reports that a group of insurgents have launched a coordinated attack and clashes are underway near a non-governmental organization.
The International Committee of the Red Cross announced in October it would "drastically" reduce its presence in the country after seven employees were killed in attacks a year ago.