Police spokesman Ebadullah Karimi said that armed men entered a building close to an installation used by Afghanistan's intelligence agency on Tuesday afternoon.
Al Jazeera reported that the attack took place at a compound in Kabul's District Eight, and gunmen had taken up positions within it.
Gunfire at the scene of the explosion was ongoing, and the Afghan government had deployed specialist troops to end the clashes.
Earlier, police officials told Al Jazeera that at least three Afghan civilians were wounded in the Shah Shaheed district of Kabul when, also in the city's east, a Taliban fighter drove a car bomb in to a NATO convoy.
Al Jazeera's Jennifer Glasse, reporting from Kabul, said the first attack, which was claimed by the Taliban, took place a few kilometres east of the centre of the city and plumes of smoke could be seen after the attack.
"Police told us that the target was a convoy, a car carrying international advisers who were not in military uniform, an armoured car," Glasse said.
The attack follows a car bomb attack on NATO soldiers last week, which killed two Afghan civilians and injured 26 others, including women and children.
NATO said none of its troops were killed or injured in last week's attack, which was also claimed by the Taliban.
A fortnight earlier, the armed group launched an attack on Afghanistan's parliament, killing five people and losing another seven of its own members.
The Taliban launched its annual spring offensive in April.
A surge in attacks has taken a heavy toll on civilians, according to the UN Assistance Mission to Afghanistan.