Elsewhere in the capital, gunfire and an explosion were heard as insurgents entered a building close to an installation used by Afghanistan's intelligence agency, a police official said. No further details were immediately available.
Taliban militants and other insurgents have stepped up attacks on Afghan and foreign forces this year, after most coalition troops withdrew from Afghanistan at the end of 2014.
Read: Pakistan rejects Afghan claims of ISI involvement in parliament attack
As security has deteriorated across the country, some districts have fallen under Taliban control. A growing presence of forces loyal to Islamic State has fuelled concern that parts of the country are slipping out of Kabul's grasp.
An Afghan security official at the scene of the convoy attack said the vehicle carrying foreign forces caught fire after the explosion in the Shah Shaheed area of eastern Kabul.
The blast blew the vehicle off course and into a wall, leaving behind an empty charred hulk.
"I can confirm that a suicide car bomber targeted foreign forces," interior ministry spokesperson Sediq Sediqqi told Reuters.
The Taliban claimed responsibility for the attack on social media website Twitter. Last Tuesday, a suicide bomber struck a convoy of US troops.
There were no fatalities from this week's attack, the coalition said in a statement, declining to give details.
"In this incident, one foreigner and one bystander were wounded," police spokesperson Ebadullah Karimi said.
Gunfire and an explosion were reported from a second attack in the city, he added. "We have reports that insurgents have entered a building," Karimi said, adding that the attack site was near an installation used by the intelligence agency.
Read: Suicide blasts hit Afghanistan as Taliban wage bloody fighting season
About 9,800 US troops remain in Afghanistan, down from a peak of around 100,000 in 2011. The majority are training Afghan forces but a few thousand are still engaged in combat operations against the Taliban and others.
On a visit to Kabul on Saturday, US Senator John McCain of Arizona called for US troops to stay longer than planned to prevent gains by the militants.
The current schedule is for the military to draw down to an embassy presence by the end of 2016.
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