A suicide bomber detonated his explosives at the gate of the compound at around 9 am local time (10.30 am Indian Standard Time).
Provincial government spokesman Attaullah Khogyani said the aid agency was targeted early on Wednesday morning.
Tolo News said 11 people had been injured.
At least 11 people were wounded in the blast that was caused by a auto bomber outside the headquarters of the NGO in the city of Jalalabad early Wednesday morning, Afghanistan's Tolo news network reported.
Security forces immediately cordoned off the area.
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Mohammad Amin, who was inside the compound when the attackers stormed inside, told AFP from his hospital bed that he heard "a big blast".
"I hope for a quick and safe end to this horrific incident", he said on Twitter. "We are awaiting further information from our team and can not further at this time", said Schuurman.
Wednesday's attack comes just days after at least 18 civilians were killed, and 22 others were wounded, during a deadly siege on a major hotel in Afghanistan's capital, Kabul.
Save the Children is one of the largest relief organizations in Afghanistan.
There are reports that a group of insurgents have launched a coordinated attack and clashes are underway near a non-governmental organization.