No group immediately claimed responsibility for the bombing, which comes as Afghan forces battle to end an hours-long siege near the Indian consulate in northern Mazar-i-Sharif city.
"A bomber on foot detonated his suicide vest... near Kabul airport. There is no immediate information on casualties," interior ministry spokesman Najib Danish told AFP.
Danish said the target was a foreign forces convoy passing through the area but a police spokesman said he was not aware of that.
The bombing marks the latest assault on the war-scarred Afghan capital.
A Taliban suicide car bomber struck a French restaurant popular with foreigners in Kabul on Friday, killing two people in a New Year's day attack.
Fifteen others were wounded in the attack on Le Jardin, an Afghan-owned eatery, which caused a piercingly loud explosion and left a building engulfed in flames.
And last Monday, a Taliban bomber detonated an explosives-packed vehicle near Kabul airport, killing one civilian in an assault targeting a NATO convoy.
The spike in violence coincides with a renewed international push to revive peace talks with the resurgent Taliban.
Afghanistan and Pakistan are set to hold a first round of dialogue between Afghanistan, Pakistan, the US and China on January 11 to lay out a comprehensive roadmap for peace.
Pakistan, which wields considerable influence over the Afghan Taliban, 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.