The suicide bomber is reported to have been driving a car laden with explosives.
Zemarai Bashary, the interior ministry spokesman, confirmed it was a suicide attack and that the target was the Nato-led International Security Assistance Force (Isaf).
"There are a number of casualties, civilians killed and wounded," he said.
Lieutenant-Commander Iain Baxter, an Isaf spokesman, said: "An Isaf convoy was hit. At the moment we're trying to confirm the number of Isaf casualties.
"We're still confirming how many Isaf casualties have been caused."
Bashary said at least 12 civilians were killed and 47 others wounded, most of whom had been travelling in a bus that passed when the suicide bomber blew up a car packed with explosives.
Children and women were among the dead and wounded, he said.
Police cordoned off the road near Darulaman palace, a derelict building that once housed Afghanistan's royal family.
Afghan television broadcast footage of the bomb site, where US soldiers and Afghan police were seen inspecting a minivan.
Al Jazeera's Hoda Abdel-Hamid, reporting from Kabul, said: "Kabul has been largely spared this continuous low-level violence that plagues the rest of the country. The last time there was a large explosion here in the capitalwas about two months ago."
Tuesday's bombing was the first major attack in Kabul since February 26 when Taliban suicide bombers targeted guesthouses, killing 16 people including Westerners and Indians in one the deadliest attacks on foreigners.
An increasingly resurgent Taliban has announced a spring offensive in May against government officials and foreign diplomats and troops.
So far this year, 202 Nato soldiers have died, marking the deadliest January to mid-May period in the Afghan war.
From January to end-May 2009, 119 Nato soldiers died in Afghanistan. Overall, 520 Nato troops died in 2009, the deadliest year so far for US-led foreign troops since the 2001 US-led invasion brought down the Taliban regime.
Since summer 2009, one or two Nato soldiers have died on average each day.