They say several other people were injured when the bomb exploded at the gates of the airport.
The Afghan Taliban have said they carried out the attack.
Afghanistan has seen days of deadly protests following the burning of Muslim holy books at a US military base near Kabul a week ago.
US officials say the books were destroyed inadvertently.
All the casualties at the airport appeared to be civilians, said provincial police official Obaidullah Talwar.
The airport serves both civilian and international military aircraft.
Meanwhile, Afghan authorities are still hunting a 25-year-old Afghan policeman believed to have shot dead two senior Nato officers at the interior ministry in Kabul on Saturday.