Four other civilians were wounded in the early morning attack, which comes amid a worsening security situation in Afghanistan as the Taliban step up their nationwide offensive.
“The bombing occurred near Kabul airport… We are finding out more details,” Gul Agha Rohani, Kabul deputy police chief, told AFP.
Interior ministry spokesman Sediq Sediqqi said on Twitter: “One civilian killed and (four) civilians wounded in today’s car bomb explosion.”
Taliban spokesman Zabiullah Mujahid said the insurgents were behind the suicide attack on a foreign forces convoy, claiming that “several invading forces were killed and wounded”.
The Taliban are known to exaggerate battlefield claims.
In a brief statement, NATO said it was investigating the incident.
The attack comes a day after Pakistan’s powerful army chief General Raheel Sharif visited Kabul in a bid to prepare the ground for fresh peace talks with the Taliban.
“Both sides agreed that the first round of dialogue between Afghanistan, Pakistan, US and China will be held in January to lay out a comprehensive roadmap for peace,” the Afghan presidential palace said in a statement.
There was no immediate reaction from the Taliban to the announcement of the four-party talks.
Asim Bajwa, a Pakistani military spokesman, said on Twitter that the talks will be held in the first week of January but did not disclose the venue.
Pakistan hosted a milestone first round of talks in July but the negotiations stalled when the insurgents belatedly confirmed the death of longtime leader Mullah Omar.
Afghanistan sees the support of longtime nemesis Pakistan as vital to bring the Taliban to the negotiating table.
But despite the growing bonhomie, analysts caution that any substantive talks are still a long way off.
Observers say the intensifying insurgency highlights a push by the militants to make more military gains in a bid to wrangle greater concessions during talks.
The offensive has prompted the first British deployment to the volatile province in 14 months.
The deployment, in addition to a recent arrival of US special forces in the region, comes a year after NATO forces formally ended their combat operations in the country.
The British and US intervention has fuelled the perception that foreign powers are increasingly being drawn back into the conflict as Afghan forces struggle to rein in the Taliban.