Militants are believed to have set off a suicide car bomb before entering the offices of Counterpoint International, resulting in a stand-off with Afghan security forces.
All five attackers were also killed in the attack and at least 200 workers were evacuated from the building.
The Taliban said the NGO was involved in “harmful Western activities”.
Security forces exchanged gunfire with insurgents in the compound in the busy Shahr Naw area of the capital city.
Afghanistan’s Ministry of Interior Affairs spokesman Nasrat Rahimi posted the number of people killed and injured on Twitter and said security forces were going through the NGO building.
“Two floors of the building have been cleared and to avoid civilian casualties, the operation is being undertaken with caution,” he said.
The attack comes amid the sixth round of talks between the US and the Taliban in Qatar, which aim to bring an end to the 18 year war.
Last week, the Taliban turned down a ceasefire agreement proposed by President Ashraf Ghani and Zalmay Khalilzad, the US special envoy for peace in the country.
Counterpart International has operated in Afghanistan since 2005 and runs civic engagement projects, supporting women and other marginalised groups.
The charity has posted a statement saying: “We are incredibly saddened by this attack and are working as quickly as possible to account for our staff. Their safety and security is our primary concern.”
Taliban spokesman Zabihullah Mujahid said Counterpart International was involved in “harmful Western activities” and the “inter-mixing” of men and women.
Before they were ousted from power in 2001, the Taliban banned women from working outside their homes and insisted they be accompanied by a male relative.
Akbar Khan Sahadat, a prosecutor in the Attorney General’s office close to the scene of the blast, told AFP how he had escaped.
“We started running out of the building and while running outside, I heard small gunfire and the sound of grenades going off nearby,” he said.
John Bass, the US Ambassador to Afghanistan, opposed the attack in a tweet, describing it as “senseless violence”.
At least 13 people were killed in an attack on a police headquarters in the northern Afghan city of Pul-e-Khumri on Monday.