The Taliban later claimed responsibility for the attack.
The Afghan police rapid action force reportedly cleared the building floor by floor. No international forces were involved in the counter-militancy operation, sources said. Seven militants were killed by the forces.
Witnesses said sounds of explosion and firing were heard from the airport early on Monday morning.
All flights in and out of Kabul were cancelled following the incident. The Afghan capital acts as a base to Nato-led military forces. Embassies in the city's diplomatic circles were also shut.
The Taliban announced a "spring offensive" two months ago, threatening to target foreign military bases and diplomatic circles. Last month, a heavy fighting broke out between the security forces and Taliban insurgents here after a major explosion took place.
Afghanistan is standing at the crossroads with the western forces preparing to pull out from its soil by the end of the next year. It will be the first time since 1992 that the indigenous forces will take responsibility for the security of the entire nation.