The Afghan Interior Ministry said that a car bomb exploded on early Monday near Kabul airport, which is used by NATO and anti-Taliban coalition forces.
The head of Kabul police, Abdul Rahman Rahimi, said one person was killed and 13 others wounded in the attack, including three women.
He claimed that the aim of attacking a predominanly civilian area is to spread fear among Afghan civilians.
No group has yet claimed responsibility for the attack.
The attack came just a day after Pakistan army chief General Raheel Sharif visited Kabul in connection with peace talks between the Taliban and Afghan government.
Pakistan hosted a crucial first round of peace talks in July but negotiations with the group froze following the confirmation of the death of leader Mullah Omar’s death.
Afghan military forces are struggling with pushing out Taliban militants who have taken control in the key Sangin district in Afghanistan's southern Helmand Province..
The suicide bombing occured followed a series of attacks this month carried out by Taliban militants including an attack on a Spanish embassy guesthose in Kabul and a suicide explosion near to Bagram air base that killed six American troops last week.