No group has so far claimed responsibility for the raid by gunmen late Saturday on the guest house run by Swedish charity Operation Mercy in the heart of the Afghan capital.
"We are investigating this as a terrorist attack," interior ministry spokesman Najib Danish told AFP, adding the identity of the attackers was not confirmed.
Kabul police chief Hassan Shah Frogh suggested the Taliban may have been behind it, but the insurgents have yet to comment on the attack.
"It is clear whenever they suffer major casualties or their commanders and high profile officials are arrested, then the Taliban resort to such action."
More From This Section
But Taliban insurgents are currently ramping up their annual spring offensive, with their strength growing more than 15 years after they were toppled from power by the US-led invasion of 2001.
Authorities in Helsinki yesterday said they had contacted the family and employer of the kidnapped Finnish woman and were investigating the incident in coordination with their counterparts in Kabul.
Operation Mercy works with local Afghan communities in areas such as reducing infant mortality and women's empowerment.
The kidnapping of foreigners has been on the rise, but the threat of abduction is even greater for Afghans.
Kabul is plagued by criminal gangs who stage abductions for ransom, often targeting foreigners and wealthy locals, and sometimes handing them over to insurgent groups.
Aid workers in particular have increasingly been casualties of a surge in violence in recent years.
Katherine Jane Wilson, a well-known Australian NGO worker, was kidnapped in April last year in the city of Jalalabad near the border with Pakistan. Wilson was released in March this year.