Taliban militants fighting to topple the foreign-backed Kabul government claimed responsibility for the attack, which followed a series of bombings in the city in August.
TV footage showed an armored vehicle from a British convoy on its side as Afghan security forces cordoned off the street in the Joi Sheer neighborhood.
"It was a suicide bombing against a foreign forces convoy in a crowded part of the city and there are casualties," said Najib Danish, deputy spokesman for the interior ministry.
Danish did not specify whether there were casualties among the foreign forces but an interior ministry statement said three civilians had been wounded, Reuters reported.
The US-led Resolute Support military coalition in Kabul confirmed that one of its convoys was struck by a bomb. "No casualties are reported at this time," said spokesman Colonel Brian Tribus.
The Taliban said Sunday's attack killed a number of foreign troops. The group typically inflates casualty figures they inflict on Afghan and coalition forces.
The attack came during a period of heightened tension following intense fighting between government troops and the Taliban around the northern city of Kunduz, which fell briefly to the extremist movement at the end of last month.